ANEOS FORSTERITE MODEL DOCUMENTATION NOTEBOOK¶
ANEOS FORSTERITE
RELEASE VERSION: SLVTv1.0G1
RELEASE DATE: 20191005
This Jupyter notebook provides documentation for a new ANEOS forsterite model EOS. This notebook is a companion to the following paper that presents modifications to the ANEOS code and new forsterite model:
Stewart, S., et al. (revised). The shock physics of giant impacts: Key requirements for the equations of state. In J. Lane, T. Germann, and M. Armstrong (Eds.), 21st Biennial APS Conference on Shock Compression of Condensed Matter (SCCM19). AIP Publishing.
When this model EOS is used, cite this paper and the doi-tagged Zenodo archive that corresponds to the release version of the forsterite EOS model. The README file in the github repository provides the history of release versions and doi numbers.
Future updates to this forsterite EOS will be archived in Zenodo doi-tagged version-controlled releases.
This notebook also highlights several technical issues that arise in developing and implementing EOS models into hydrocodes. We introduce two tabulated quality parameters to help guide usage of this EOS model.
Sarah T. Stewart
sts@ucdavis.edu
October 5, 2019
Documentation updated October 9, 2019
VERSION INFORMATION
Forsterite EOS Version: Forsterite-ANEOS-SLVTv1.0G1
SLVT# translates to solid-liquid-vapor-thermal model adjustment-version number
G1 = the gridded EOS tables used the gridflag=1 definition for the grid points
SLVTv1.0G1 Release Date: 10/05/2019
GitHub: https://github.com/ststewart/aneos-forsterite-2019/
This is a solid-liquid-vapor ANEOS model with ionization for pure forsterite (Mg$_2$SiO$_4$). This model EOS uses the new heat capacity adjustment factor described in Stewart et al. (SCCM19) and Stewart, ANEOS Code Modification: Thermal model adjustment parameter, https://github.com/ststewart/aneos-forsterite-2019/EOS-docs/, 2019.
This Jupyter notebook was used to develop and document new ANEOS input parameters for the forsterite EOS that are optimized for the liquid and vapor regions. This development project focused on improving the forsterite model EOS for impact simulations where the silicate is melted and partially vaporized upon shock and decompression.
This notebook also reproduces the figures in Stewart et al. (SCCM19). The figures include a comparison to the Tillotson EOS, so this notebook also includes Tillotson EOS functions based on the implementations in iSALE-Dellen (https://isale-code.github.io/) and Hosono et al. (2019).
A reference list is provided at the end of this notebook. PDFs of some of the open access references are included in the github repository.
USAGE
This notebook interacts with multiple outputs from ANEOS, including phase boundary information, the calculated Hugoniot, and tabulated EOS. The notebook also reads in material properties data and extracted data from previous versions of ANEOS model parameter sets for forsterite.
This notebook is designed to be used in two modes:
- Development mode: ANEOS is called in the local directory to generate new model output. The user can varying the model input parameters and tabular gridding schemes. This notebook produces plots of the equation of state surface and comparisons to experimental data and ab initio calculations.
- Release mode: the notebook interacts with previously created ANEOS model output. This notebook provides detailed documentation of a version-controlled release of the model EOS and enables users to interact with the EOS surface and compare the model to data.
This notebook is distributed in release mode. Users who wish to use the development mode may request the modified version of ANEOS from the author.
Development mode:
The notebook calls a local aneos executable which expects a formatted ANEOS.INPUT ascii file and an ascii gridtable.txt definition file that is generated by this notebook. ANEOS produces an ANEOS.OUTPUT ascii file and gridded ascii SESAME-format EOS tables.
The user edits (1) the input parameters in ANEOS.INPUT (separately from this notebook) and (2) the output EOS table parameters in the notebook cell below.
This notebook reads some parameters from ANEOS.INPUT and assumes that the variables are spaced by 10 columns.
When the notebook is run, the code issues a system call to run the aneos program in the local directory and reads in results from the ANEOS.OUTPUT, NEW-SESAME-STD.TXT, and NEW-SESAME-EXT.TXT files to make the plots below and to generate the GADGET format EOS table and other miscellaneous files.
Release mode:
This notebook reads in the provided ANEOS.INPUT, EOS tables, and other distribution data to generate the plots below.
OUTPUT/PROVIDED DATA FILES
ANEOS.OUTPUT: Plain text file with an overview of the calculated equation of state. Look at this file for any errors in the EOS calculation.
NEW-SESAME-STD.TXT: Standard length Sandia-style SESAME file with 201 table and 301 table (density, temperature, pressure, sp. internal energy, Helmholtz free energy). 301 table units: g/cm$^3$, K, GPa, MJ/kg, MJ/kg.
NEW-SESAME-EXT.TXT: SESAME-style table with extra variables from ANEOS. Contains the standard 201 table and non-standard 301-extra-variables EOS table. The 301 table has: density grid values, temperature grid values, sp. entropy(T,rho), sound speed(T,rho), sp. heat capacity(T,rho), KPA flag(T,rho). 2-D arrays list all densities, looping over each temperature. 301 table units: g/cm$^3$, K, MJ/K/kg, cm/s, MJ/K/kg, integer flag, integer flag. The KPA flag is an ANEOS output with phase information.
NEW-SESAME-HUG.TXT: Ascii table with the reference state Hugoniot.
NEW-SESAME-MDQ.TXT: Ascii 301-style SESAME table with the MDQ rating.
NEW-SESAME-IEP-BILINEAR.TXT: Standard length Sandia-style SESAME file with 201 table and 301-style table containing the IEP values for bilinear interpolation. Format: 1-D interpolated density points, 1-D interpolated temperature points, 2-D IEP arrays for pressure, sp. internal energy, Helmholtz free energy, sound speed). IEP units are ratios to the original calculated ANEOS point values. Located in the interpolation subdirectory.
NEW-SESAME-STD-NOTENSION.TXT: Standard length Sandia-style SESAME file with 201 table and 301 table (density, temperature, pressure, sp. internal energy, Helmholtz free energy) where the ANEOS tension region is removed and replaced with the solid-vapor coexistence region. 301 table units: g/cm$^3$, K, GPa, MJ/kg, MJ/kg.
NEW-GADGET2-STD-NOTENSION.TXT: Standard GADGET2 EOS table generated by interpolating the ANEOS table with no tension. Format: number of density points, number of sp. entropy points, density grid values, sp. entropy grid values, 2-D arrays of pressure, temperature, specific internal energy, sound speed. 2-D array values list all densities, looping over each value for specific entropy. Units: g/cm$^3$, erg/K/g, dynes/cm$^2$, K, erg/g, cm/s.
NEW-GADGET2-EXT-NOTENSION.TXT: Extended variables GADGET2 EOS table generated by interpolating the ANEOS table with no tension. Format: number of density points, number of sp. entropy points, density grid values, sp. entropy grid values, 2-D arrays of Helmholtz free energy, KPA flag, MDQ flag. 2-D array values list all densities, looping over each value for specific entropy. Units: g/cm$^3$, erg/K/g, erg/g, integer flag, integer flag.
The SESAME tabular equation of state formats are described in Lyon and Johnson (1992).
APPLICATIONS AND LIMITATIONS
The reference state is the solid at STP. As a compromise to span the whole phase diagram, the reference bulk modulus is lower than the true value at STP. The Debye temperature is fitted to attain the true specific entropy at melting with a single solid phase. The heat capacity adjustment parameter is set to 1.35 to fit the temperatures and entropies on the shock Hugoniot and liquid heat capacity at 1 bar.
This EOS table is appropriate for problems where forsterite/olivine is present as a warm solid near the melt curve, liquid, and partially vaporized. The temperatures in the liquid field are much improved with the adjusted heat capacity. The critical point is much improved over previous version of forsterite ANEOS used in modeling impact processes. The bulk modulus is a compromise to produce a model that spans a wide range of P-V-T and accommodates the limitations of the formulas used for the Gruneisen parameter in ANEOS.
This model does not include a high-pressure phase transition to avoid the artificial discontinuities introduced in the liquid field by ANEOS. This model becomes increasingly erroneous for shock pressures above about 1000 GPa as the curvature on the Hugoniot and the Grueneisen parameter are not correct at extremely high densities.
This model is not appropriate for problems entirely in solid forsterite. The modulus of the solid is low and high-pressure polymorphs are neglected.
The functional form for the Gruneisen parameter in ANEOS has difficulty matching the experimental values for liquid forsterite.
The interpolation procedure to make the GADGET2 density-entropy-grid table uses linear interpolation on the same density grid as the density-temperature SESAME table to obtain the EOS values at each GADGET2 entropy grid point. This method introduces substantial errors in the vapor dome.
MODEL DEVELOPMENT QUALITY (MDQ) RATING
We provide an MDQ rating which is saved as a 301-style SESAME table. The MDQ rating is a qualitative guide for users that provides some known quality control information. This information is necessarily subjective and incomplete. The rating does not guarantee any fidelity in the EOS model except for points that have been directly compared to experimental data in the plots below. See discussion with the plots below.
INTERPOLATION ISSUES AND THE INTERPOLATION ERROR PARAMETER (IEP)
The IEP measures the quality of the interpolation scheme for a specific variable on a specific density-temperature grid. Robust interpolation of wide-ranging EOS tables is known to be a difficult problem. Most interpolation schemes individually interpolate each variable, which leads to interpolated states that are not thermodynamically self-consistent. While some thermodynamically consistent interpolation schemes have been developed (e.g., Zeman et al. 2019), they more computationally intensive than simpler interpolation methods and have not been widely implemented yet.
The IEP is calculated on the density-temperature grid using the following method:
- Start with a grid that is twice as dense as the desired final grid and generate an ANEOS density-temperature table.
- Split the table into two tables made from the even rows and columns and the odd rows and columns.
- Interpolate for the odd index grid values using the even index table.
- The IEP is given by (interpolated value-original value)/(original value) of the odd index table.
A tabulated EOS must be sufficiently densely gridded to capture the phase boundaries. Otherwise, non-physical material response can arise during problems that cross the phase boundary. Simple interpolations schemes generally produce large errors in and near phase boundaries. See illustrative plots below.
We recommend that the interpolation scheme, the implementation of the scheme into EOS code functions (e.g., the source code), and IEP values should be reported in published works that use tabular EOS. See the Jupyter Notebook in the subdirectory and the plots below.
ANEOS NOTES
The ANEOS source code was provided by Jay Melosh and Gareth Collins. This version included Melosh's (2007) treatment for molecular gas and the capability to include a melt curve and solid-solid/liquid-liquid transition (Collins & Melosh LPSC 2014).
In this work, Melosh and Collins version of ANEOS was modified to adjust the Debye model for the thermal term in the Helmholtz free energy to approach a user-defined heat capacity at high temperatures. The multiplicative factor $f_{cv}$ is entered in input value V44, and the high-temperature heat capacity is $3f_{cv}Nk$.
The ANEOSTEST.f routine was modified to output tabulated EOS. Note that the current version of this function sets positive pressures smaller than 1.E-30 GPa equal to 1.E-30 GPa.
ANEOS2.f was modified to increase the number of points tabulated on the melt curve in the ANEOS.OUTPUT file and to gather the variables for the heat capacity modification.
ANHUG.f was modified to output more Hugoniot points.
ANEOS1.f and ANEOS2.f were modified to increase the high temperature limit for the heat capacity (Stewart et al., SCCM19).
FUTURE DEVELOPMENTS
- Add information to MDQ to identify regions with experimental validation.
- Add binary format output for EOS tables.
- Examine other table interpolation schemes, including thermodynamically self-consistent schemes such as Zeman et al. (2019).
- Unpublished EOS data were used in the development of this model EOS. These data will be added to future versions of this model development notebook when published.
- Try rational function interpolation method of Kerley (1977) on the original density-temperature-grid table.
- Plots of free energy terms.
- Currently, SESAME ascii file sizes are limited by github. Future releases will use binary SESAME files.
CORRECTIONS AND IMPROVEMENTS
Please send corrections to STS and any requests for data to include in the model-data comparison plots.
In [1]:
# this cell has a java script that that enables hiding the raw python code
from IPython.display import HTML
HTML('''<script>
code_show=true;
function code_toggle() {
if (code_show){
$('div.input').hide();
} else {
$('div.input').show();
}
code_show = !code_show
}
$( document ).ready(code_toggle);
</script>
<form action="javascript:code_toggle()"><input type="submit" value="Click here to toggle on/off the raw code."></form>''')
Out[1]:
In [2]:
# Record the verions information for these calculation for posterity
import platform
print('python version: ',platform.python_version())
del platform
import matplotlib
print('matplotlib version: ', matplotlib.__version__)
del matplotlib
import numpy
print('numpy version: ', numpy.__version__)
del numpy
import scipy
print('scipy version: ', scipy.__version__)
del scipy
import pandas
print('pandas version: ', pandas.__version__)
del pandas
# this prevents some error messages for inline plotting in a jupyter notebook
%matplotlib inline
# import python libraries
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import matplotlib.colors as colors
from mpl_toolkits.axes_grid1 import make_axes_locatable
from copy import deepcopy
import numpy as np
from scipy import interpolate
import colormaps as local_cmaps
import subprocess
import pandas as pd
from matplotlib.collections import PatchCollection
from matplotlib.patches import Rectangle
#
plt.rcParams["figure.figsize"] = (20,10)
plt.rcParams["patch.force_edgecolor"] = True
USER INPUTS FOR SESAME AND GADGET2 TABLE CONSTRUCTION¶
If the code cell below is hidden, use the button above to reveal the cell.
In development mode, the user must input:
- Header information for the SESAME table.
- Temperature, density and entropy grid points.
The following code cell also includes the development mode flag and option to skip construction of a GADGET2 table if it is not needed.
In [3]:
# -------------------------------------------------------------
# USER INPUTS
#-------------------------------------------------------------
# NOTEBOOK MODE
#-------------------------------------------------------------
#
DEVMODE = 0 # 1=development mode; 0=release mode
#
#-------------------------------------------------------------
# OPTIONS TO REMOVE TENSION REGION AND CONSTRUCT A GADGET2 TABLE
#-------------------------------------------------------------
#
REMOVETENSIONFLAG=1 # 0- keep tension region; 1- remove tension region
MAKEGADGETTABLE=1 # 1=make table; 0=do not make gadget2 table
#
#-------------------------------------------------------------
# USER MUST SET THESE VALUES TO DEFINE THE TABULATED EOS GRIDS
#-------------------------------------------------------------
#
# ====>>>>>> YOU NEED TO MAKE SURE THESE VALUES MATCH ANEOS.INPUT <<<<=====
MODELNAME = 'Forsterite-ANEOS-SLVTv1.0G1'
# Header information must all be compatible with float format
MATID = 1.0 # MATID number
DATE = 190802. # Date as a single 6-digit number YYMMDD
VERSION = 0.1 # ANEOS Parameters Version number
FMN = 70. # Formula weight in atomic numbers for Mg2SiO4
FMW = 140.691 # Formula molecular weight (g/cm3) for Mg2SiO4
# The following define the default initial state for material in the 201 table
R0REF = 3.22 # g/cm3 *** R0REF is inserted into the density array
K0REF = 1.1E12 # dynes/cm2
T0REF = 298. # K -- *** T0REF is inserted into the temperature array
P0REF = 1.E6 # dynes/cm2 -- this defines the principal Hugoniot calculated below
#
# generate output files for other ANEOS models
modelflag = 0 # 0 - don't change anything above; 1 - Canup et al. 2013;
# 2 - GADGET2 Marcus PhD Thesis & Cuk & Stewart 2012; 3 - ISALE Dellen Collins and Melosh 2014
#
if modelflag == 1:
MODELNAME = 'Canup2013 Forsterite'
# Header information must all be compatible with float format
MATID = 1.0 # MATID number
DATE = 190802. # Date as a single 6-digit number YYMMDD
VERSION = 1.0 # ANEOS Parameters Version number
FMN = 70. # Formula weight in atomic numbers for Mg2SiO4
FMW = 140.691 # Formula molecular weight (g/cm3) for Mg2SiO4
# The following define the default initial state for material in the 201 table
R0REF = 3.32 # g/cm3 *** R0REF is inserted into the density array
K0REF = 1.446E12 # dynes/cm2 K0=rho0*cs0^2
T0REF = 298. # K -- *** T0REF is inserted into the temperature array
P0REF = 1.E6 # dynes/cm2 -- this defines the principal Hugoniot calculated below
if modelflag == 2:
MODELNAME = 'GADGET2 Forsterite'
# Header information must all be compatible with float format
MATID = 1.0 # MATID number
DATE = 190802. # Date as a single 6-digit number YYMMDD
VERSION = 1.0 # ANEOS Parameters Version number
FMN = 70. # Formula weight in atomic numbers for Mg2SiO4
FMW = 140.691 # Formula molecular weight (g/cm3) for Mg2SiO4
# The following define the default initial state for material in the 201 table
R0REF = 3.32 # g/cm3 *** R0REF is inserted into the density array
K0REF = 1.446E12 # dynes/cm2 K0=rho0*cs0^2
T0REF = 298. # K -- *** T0REF is inserted into the temperature array
P0REF = 1.E6 # dynes/cm2 -- this defines the principal Hugoniot calculated below
if modelflag == 3:
MODELNAME = 'ISALE Forsterite'
# Header information must all be compatible with float format
MATID = 1.0 # MATID number
DATE = 190802. # Date as a single 6-digit number YYMMDD
VERSION = 1.0 # ANEOS Parameters Version number
FMN = 70. # Formula weight in atomic numbers for Mg2SiO4
FMW = 140.691 # Formula molecular weight (g/cm3) for Mg2SiO4
# The following define the default initial state for material in the 201 table
R0REF = 3.227 # g/cm3 *** R0REF is inserted into the density array
K0REF = 1.336E12 # dynes/cm2 K0=rho0*cs0^2
T0REF = 298. # K -- *** T0REF is inserted into the temperature array
P0REF = 1.E6 # dynes/cm2 -- this defines the principal Hugoniot calculated below
#
#-------------------------------------------------------------
# EXAMPLE EOS GRID ARRAYS
#-------------------------------------------------------------
#
# Life is easier if the grid arrays are even in length (after adding T0REF and R0REF below)
#
# Flag for easily switching between different table grids during model development
# 0: low res for testing
# 1: high res for production: release version SLVT1.0G1
gridflag = 1
#
#------------------------------------------------------
if gridflag == 99: # low res for testing
gridtvals = [0, 10000., 20000.,1.e7] # K -- this array defines the edges of the segments along the grid, 0 is changed to 1 below
gridtstyle = [1,1,0] # 1 for linear, 0 for log in each segment
gridtnpts = [30., 30.,20.] # number of grid points in each segment
# define the density array for the SESAME AND GADGET2 tables
gridrvals = [1.e-20, 0.1, 2.6, 3.2, 10., 30.] # g/cm3 -- this array defines the edges of the segments along the grid
gridrstyle = [0, 1, 1, 1, 1] # 1 for linear, 0 for log in each segment
gridrnpts = [20, 10, 6, 30, 20] # number of grid points in each segment
# define the specific entropy array for the GADGET2 table
gridsvals = [1.e-4,.25] # MJ/K/kg -- this array defines the edges of the segments along the grid
gridsstyle = [0] # 1 for linear, 0 for log in each segment
gridsnpts = [80] # number of grid points in each segment
#
if gridflag == 0: # medium resolution grid <1E7 entries in 301 table. This is about 250,000 values.
# define the temperature array for the SESAME table
# 0 K is changed to 1 K
# 298 K is inserted into the table if it is not present in the original array
gridtvals = [0, 10000., 20000.,1.e7] # K -- this array defines the edges of the segments along the grid, 0 is changed to 1 below
gridtstyle = [1,1,0] # 1 for linear, 0 for log in each segment
gridtnpts = [200.,200.,150.] # number of grid points in each segment
# define the density array for the SESAME AND GADGET2 tables
# 0 g/cm3 is removed if present
gridrvals = [1.e-20, 0.1, 2.6, 3.2, 10., 30.] # g/cm3 -- this array defines the edges of the segments along the grid
gridrstyle = [0, 1, 1, 1, 1] # 1 for linear, 0 for log in each segment
gridrnpts = [150, 76, 54, 206, 40] # number of grid points in each segment
# define the specific entropy array for the GADGET2 table
# 0 MJ/K/kg is removed if present
gridsvals = [0.,0.03] # MJ/K/kg -- this array defines the edges of the segments along the grid
gridsstyle = [1] # 1 for linear, 0 for log in each segment
gridsnpts = [500] # number of grid points in each segment
#
if gridflag == 1: # new form for the high resolution table entries in 301 table. Try for 1e6 values
# define the temperature array for the SESAME table
# 0 K is changed to 1 K
# T0REF is inserted into the table if it is not present in the original array
# need to have extra temperature resolution around the triple point
gridtvals = [0, 100, 2000, 2300, 10000., 20000.,1.e7] # K -- this array defines the edges of the segments along the grid, 0 is changed to 1 below
gridtstyle = [1,1,1,1,1,0] # 1 for linear, 0 for log in each segment
gridtnpts = [2, 191., 100, 300.,100.,50.] # number of grid points in each segment
# define the density array for the SESAME AND GADGET2 tables
# R0REF is inserted into the table if it is not present in the original array
# need to have extra density resolution around the triple point
# 0 g/cm3 is removed if present
gridrvals = [1.e-20, 0.1, 2.6, 3.4, 10., 30.] # g/cm3 -- this array defines the edges of the segments along the grid
gridrstyle = [0, 1, 1, 1, 1] # 1 for linear, 0 for log in each segment
gridrnpts = [200, 100, 160, 300, 100] # number of grid points in each segment
# define the specific entropy array for the GADGET2 table
# 0 MJ/K/kg is removed if present
gridsvals = [1.e-4,.25] # MJ/K/kg -- this array defines the edges of the segments along the grid
gridsstyle = [0] # 1 for linear, 0 for log in each segment
gridsnpts = [800] # number of grid points in each segment
#----------------------------------------
# END USER INPUT
#----------------------------------------
In [4]:
# THIS CELL DEFINEs FUNCTIONS
# define index function (must be a more efficient way to do this...)
get_indexes = lambda x, xs: [i for (y, i) in zip(xs, range(len(xs))) if x == y]
#
# LOAD EXTERNAL FUNCTIONS AND OBJECT CLASSES
# defines rational function interpolation functions rf1d and rf2d
#%run rfinterpolation.py
# defines class objects for extEOStable and functions to read in ANEOS input and output
# READ THIS CODE IF YOU WANT TO UNDERSTAND THE FILE STRUCTURES
%run eostable.py
# Run the following help for the functions in the class
#help(extEOStable())
In [5]:
# THIS CELL HAS CODE TO GENERATE THE GRIDS AND WRITES TO A FILE TO BE READ BY ANEOS
print('GENERATING ARRAYS FOR THE INDICES OF THE TABULATED EOS.')
#-------------- the following code generates the temperature array
gridtarr = []
for iir in range(1,len(gridtvals)):
if gridtstyle[iir-1] == 1:
# linear region
temptarr = np.arange(gridtnpts[iir-1])/gridtnpts[iir-1]*(gridtvals[iir]-gridtvals[iir-1])+gridtvals[iir-1]
if gridtstyle[iir-1] == 0:
# log region
logstep = (np.log10(gridtvals[iir])-np.log10(gridtvals[iir-1]))/gridtnpts[iir-1]
temptarr = np.power(10.,np.log10(gridtvals[iir-1])+(np.arange(gridtnpts[iir-1]))*logstep)
gridtarr = np.concatenate((gridtarr,temptarr))
# check if T0REF already in the grid
#indexT0REF = get_indexes(T0REF,gridtarr)
indexT0REF = np.where(abs(T0REF-gridtarr)<1.E-4)[0]
if len(indexT0REF) == 0:
# insert T0REF K into the array
indexT0REF = np.where((gridtarr-T0REF)>0.)[0]
gridtarr = np.concatenate((gridtarr[0:indexT0REF[0]],[T0REF],gridtarr[indexT0REF[0]::]))
if indexT0REF[0]>1:
print('Inserted the REFERENCE TEMPERATURE INTO THE ARRAY:',gridtarr[indexT0REF[0]-2:indexT0REF[0]+3])
else:
print('Inserted the REFERENCE TEMPERATURE INTO THE ARRAY:',gridtarr[indexT0REF[0]-1:indexT0REF[0]+3])
else:
print('T0REF already in temperature array: ',T0REF,gridrarr[indexT0REF[0]-2:indexT0REF[0]+2])
# Remove 0 K or convert to 1 K
indexzero = get_indexes(0.,gridtarr)
indexone = get_indexes(1.,gridtarr)
if len(indexzero) == 1 and len(indexone) == 0:
gridtarr[indexzero] = 1.
print('Zero kelvin changed to 1 kelvin.')
else:
gridtarr = np.delete(gridtarr, indexzero)
print('Deleted zero K index.')
#
#gridtsize = len(grdtarr)
print('Number of temperature points: ',len(gridtarr))
#print(gridtarr)
#------------ the following code generates the density array
gridrarr = []
for iir in range(1,len(gridrvals)):
if gridrstyle[iir-1] == 1:
# linear region
temprarr = np.arange(gridrnpts[iir-1])/gridrnpts[iir-1]*(gridrvals[iir]-gridrvals[iir-1])+gridrvals[iir-1]
if gridrstyle[iir-1] == 0:
# log region
logstep = (np.log10(gridrvals[iir])-np.log10(gridrvals[iir-1]))/gridrnpts[iir-1]
temprarr = np.power(10.,np.log10(gridrvals[iir-1])+(np.arange(gridrnpts[iir-1]))*logstep)
gridrarr = np.concatenate((gridrarr,temprarr))
# check if R0REF already in the grid
#indexR0REF = get_indexes(R0REF,gridrarr)
indexR0REF = np.where(abs(R0REF-gridrarr)<1.E-4)[0]
if len(indexR0REF) == 0:
# insert R0REF into the array
indexR0REF = np.where((gridrarr-R0REF)>0.)[0]
gridrarr = np.concatenate((gridrarr[0:indexR0REF[0]],[R0REF],gridrarr[indexR0REF[0]::]))
print('Inserted the REFERENCE DENSITY INTO THE ARRAY:',gridrarr[indexR0REF[0]-2:indexR0REF[0]+3])
#print('NOT INSERTING REFERENCE DENSITY INTO THE ARRAY.')
else:
print('R0REF already in density array: ',R0REF,gridrarr[indexR0REF[0]-2:indexR0REF[0]+2])
# Remove 0 g/cm3 if present
indexzero = get_indexes(0.,gridrarr)
if len(indexzero) == 1:
gridrarr = np.delete(gridrarr, indexzero)
print('Deleted zero g/cm3 index.')
#
#gridrsize = len(gridrarr)
print('Number of density points: ',len(gridrarr))
#print(gridrarr)
#------------ the following code generates the specific entropy array for gadget tables
gridsarr = []
for iir in range(1,len(gridsvals)):
if gridsstyle[iir-1] == 1:
# linear region
tempsarr = np.arange(gridsnpts[iir-1])/gridsnpts[iir-1]*(gridsvals[iir]-gridsvals[iir-1])+gridsvals[iir-1]
if gridsstyle[iir-1] == 0:
# log region
logstep = (np.log10(gridsvals[iir])-np.log10(gridsvals[iir-1]))/gridsnpts[iir-1]
tempsarr = np.power(10.,np.log10(gridsvals[iir-1])+(np.arange(gridsnpts[iir-1]))*logstep)
gridsarr = np.concatenate((gridsarr,tempsarr))
# Remove 0 MJ/K/kg if present
indexzero = get_indexes(0.,gridsarr)
if len(indexzero) == 1:
gridsarr[indexzero]=1.e-20
# gridsarr = np.delete(gridsarr, indexzero)
print('replaced zero MJ/K/kg index with 1.E-20')
#gridssize = len(gridsarr)
#
print('Number of specific entropy points: ',len(gridsarr))
#print(gridsarr)
print('Number of words in the standard SESAME 301 table (NR, NT, R, T, P, IE, HFE)=',2.+len(gridrarr)+len(gridtarr)+len(gridrarr)*len(gridtarr)*3.)
#-----------------------------------------------------------
#
if DEVMODE:
print('WRITING tablegrid.txt FOR ANEOS in the local directory.\n')
# write the table arrays to a file for the ANEOS driver to read in
tablegridfile = open("tablegrid.txt","w")
tablegridfile.write("{:.6e}".format(MATID)+'\n')
tablegridfile.write("{:.6e}".format(DATE)+'\n')
tablegridfile.write("{:.6e}".format(VERSION)+'\n')
tablegridfile.write("{:.6e}".format(FMN)+'\n')
tablegridfile.write("{:.6e}".format(FMW)+'\n')
tablegridfile.write("{:.6e}".format(R0REF)+'\n')
tablegridfile.write("{:.6e}".format(K0REF)+'\n')
tablegridfile.write("{:.6e}".format(T0REF)+'\n')
tablegridfile.write("{:.6e}".format(len(gridrarr))+'\n') # number of density points
tablegridfile.write("{:.6e}".format(len(gridtarr))+'\n') # number of temperature points
for i in range(0,len(gridrarr)):
tablegridfile.write("{:.6e}".format(gridrarr[i])+'\n')
for i in range(0,len(gridtarr)):
tablegridfile.write("{:.6e}".format(gridtarr[i])+'\n')
tablegridfile.close()
#
#-----------------------------------------------------
# Output GADGET2 Table information
if MAKEGADGETTABLE:
print('Number of words in the extended GADGET2 EOS table (NR, NS, R, S, P, T, IE, CS, HFE, CV, KPA, MDQ)=',2.+len(gridrarr)+len(gridtarr)+len(gridrarr)*len(gridtarr)*8.)
#------------------------------------------------------
#----------------------------------------------------
# Sp. Internal Energy grid for Tillotson
tillearr = np.power(10.,np.arange(600)/600.*6.-3.) # MJ/kg
tillearr = np.append(0.,tillearr)
print('Number of specific internal energy points for Tillotson EOS: ',len(tillearr))
#----------------------------------------------------
# Paranoia check
# make sure all table grid values are unique
if (len(np.unique(gridtarr))!=len(gridtarr)):
print('NON-UNIQUE VALUES IN TEMP ARRAY')
stopthecode
if (len(np.unique(gridrarr))!=len(gridrarr)):
print('NON-UNIQUE VALUES IN DENSITY ARRAY')
stopthecode
if (len(np.unique(gridsarr))!=len(gridsarr)):
print('NON-UNIQUE VALUES IN SP. ENTROPY ARRAY')
stopthecode
if (len(np.unique(tillearr))!=len(tillearr)):
print('NON-UNIQUE VALUES IN SP. ENERGY ARRAY')
stopthecode
#----------------------------------------------------
print('\nDone generating EOS grids.\n')
print('\nCHECK THAT THE GRID ARRAYS ARE EVEN IN LENGTH.\n')
# END TABLE GRIDDING INFORMATION
In [6]:
if DEVMODE:
# call aneos in the local directory
# output file is in the local directory
print('RUNNING IN DEVELOPMENT MODE')
print('Calling aneos in the local directory.')
completed = subprocess.run(['./aneos'])
print('Aneos call complete. CHECK THAT A NEW ANEOS.OUTPUT FILE WAS CREATED.')
print('aneos call result: ', completed.returncode)
print('Check ANEOS.OUTPUT file for errors.')
else:
print('RUNNING IN RELEASE MODE: NO ANEOS SYSTEM CALL.')
print('READING IN EOS DISTRIBUTION FILES.')
In [7]:
# READ IN NEW ANEOS MODEL and fill the extEOStable class object
# source in eostable.py
#------------------------------------------------------------------
NewEOS = extEOStable() # FIRST make new empty EOS object
NewEOS.loadextsesame('NEW-SESAME-EXT.TXT') # LOAD THE EXTENDED 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
NewEOS.loadstdsesame('NEW-SESAME-STD.TXT') # LOAD THE STANDARD 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
NewEOS.MODELNAME = MODELNAME # string set above in user input
NewEOS.MDQ = np.zeros((NewEOS.NT,NewEOS.ND)) # makes the empty MDQ array
#print(NewEOS.units) # these are the default units for SESAME rho-T tables
#'Units: g/cm3, K, GPa, MJ/kg, MJ/kg, MJ/K/kg, cm/s, MJ/K/kg, KPA flag. 2D arrays are (NT,ND).'
# Add the header info to the table. This could be done during the loading.
# if made from this notebook, these values are set in the user-input above.
# ** MAKE SURE THEY MATCH ANEOS.INPUT **
NewEOS.MATID = MATID
NewEOS.DATE = DATE
NewEOS.VERSION = VERSION
NewEOS.FMN = FMN
NewEOS.FMW = FMW
NewEOS.R0REF = R0REF
NewEOS.K0REF = K0REF
NewEOS.T0REF = T0REF
NewEOS.P0REF = P0REF
#
# Load the information from ANEOS.INPUT and ANEOS.OUTPUT
NewEOS.loadaneos(aneosinfname='ANEOS.INPUT',aneosoutfname='ANEOS.OUTPUT')
#
# calculate the principal Hugoniot from the table
if DEVMODE:
# calculate the Hugoniot and write to a file
NewEOS.calchugoniot(r0=NewEOS.R0REF,t0=NewEOS.T0REF,writefilename='NEW-SESAME-HUG.TXT')
else:
# just calculate the Hugoniot and put it in the EOS object
NewEOS.calchugoniot(r0=NewEOS.R0REF,t0=NewEOS.T0REF)
#
# calculate the 1-bar profile; loop over temp
NewEOS.onebar.T = np.zeros(NewEOS.NT)
NewEOS.onebar.S = np.zeros(NewEOS.NT)
NewEOS.onebar.rho = np.zeros(NewEOS.NT)
it0 = np.where(NewEOS.T >= NewEOS.T0REF)[0]
id0 = np.arange(NewEOS.ND)#np.where(NewEOS.rho >= 0.8*NewEOS.R0REF)[0]
for iit in range(0,NewEOS.NT):
NewEOS.onebar.T[iit] = NewEOS.T[iit]
NewEOS.onebar.S[iit] = np.interp(1.E-4,NewEOS.P[iit,id0],NewEOS.S[iit,id0])
NewEOS.onebar.rho[iit] = np.interp(1.E-4,NewEOS.P[iit,id0],NewEOS.rho[id0])
#print(iit,NewEOS.onebar.rho[iit],NewEOS.onebar.T[iit],NewEOS.onebar.S[iit]*1.E3)
In [ ]:
In [8]:
#--------------------------------------------------------------------------
# Identify poor regions of the EOS table: SET THE MDQ FLAG
# MDQ=-5 means that there are much better model EOS formulations for these regions of phase space
#
# very high pressures and densities are known to be bad because of the gamma function values used in this model
badind = np.where(np.reshape(NewEOS.P,NewEOS.ND*NewEOS.NT) > 1000.0) # GPa
MDQtmp = np.reshape(NewEOS.MDQ,NewEOS.ND*NewEOS.NT)
MDQtmp[badind] = -5
# high-pressure solid is known to be a problem because no high-pressure phase transition
badind = np.where((np.reshape(NewEOS.P,NewEOS.ND*NewEOS.NT) > 23.0)&(np.reshape(NewEOS.KPA,NewEOS.ND*NewEOS.NT)==4)) # GPa
MDQtmp[badind] = -4
# so the high-pressure solid melt curve is also a problem
badind = np.where((np.reshape(NewEOS.P,NewEOS.ND*NewEOS.NT) > 23.0)&(np.reshape(NewEOS.KPA,NewEOS.ND*NewEOS.NT)==5)) # GPa
MDQtmp[badind] = -4
#
# return MDQ to the proper shape
NewEOS.MDQ = np.reshape(MDQtmp,(NewEOS.NT,NewEOS.ND))
#
In [9]:
# Make a NOTENSION TABLE and GADGET TABLE
################### REMOVE TENSION REGION ###########################
## The GADGET2 tables do not have a tension region.
## If the gadget2 table is selected, then must generate a no-tension table
if MAKEGADGETTABLE:
REMOVETENSIONFLAG=1 # 0- keep tension region; 1- remove tension region
# minimum pressure 1.E-30
# minimum sp energy about 1.E-4 before negative entropy region
# minimum sp entropy about 1.E-5 before negative entropy region
# minimum HFE about 1.E-3 before negative entropy region
# minimum sound speed about 1.E-10 before negative entropy region
# minimum sp heat capacity about 1.E-4 before negative entropy region
## FUTURE WORK: THIS SECTION COULD USE THE LEVER RULE TO FILL IN THE MISSING POINTS
## SINCE MANY VALUES ARE NEAR THE LOWER LIMITS IN THE SUBLIMATION REGION ANYWAY,
## HERE, TENSION REGION VALUES ARE FILLED IN WITH THE ADJACENT S-V DOME VALUES
## This is obviously bad for interpolations. Fix for future work.
if REMOVETENSIONFLAG:
# First make a deep copy of the original table with the tension region
NewEOSorig = deepcopy(NewEOS)
NewEOS.MODELNAME = NewEOS.MODELNAME+'notension'
# THIS SECTION REWRITES NEGATIVE PRESSURE REGION
# The tension region is in the solid-vapor phase boundary.
# Use the liquid-vapor phase boundary. Below the temperature of the triple point, it is the sublimation curve.
# But the pressures for the solid calculation is spurious at very low pressures, so use the vapor pressure.
# HFE = GFE + TS
print('REMOVING TENSION REGION FROM THE ORIGINAL ANEOS TABLE.')
for itt in range(NewEOS.NT-1,-1,-1):
tmp = np.where(NewEOS.P[itt,:] < 0.)
if (len(tmp[0]) > 0):
badind = tmp[0]
if badind[0] > 0:
#print(itt, len(badind), NewEOS.T[itt], 'tension only', NewEOS.P[itt,badind[0]-4:badind[0]+1])
# at this temperature, all densities are the same pressure in the vapor dome
# so use the adjacent positive pressure value
# do the same for all the variables since there is very little change in this region of the dome.
# Errors introduced by interpolating the vapor curve are comparable to
# recalculating the lever rule. Would need to call ANEOS again to get good end point values
# to calculate the mass-weighted value via the lever rule.
NewEOS.P[itt,badind] = np.full(len(badind),NewEOS.P[itt,badind[0]-1])
NewEOS.U[itt,badind] = np.full(len(badind),NewEOS.U[itt,badind[0]-1])
NewEOS.S[itt,badind] = np.full(len(badind),NewEOS.S[itt,badind[0]-1])
NewEOS.A[itt,badind] = np.full(len(badind),NewEOS.A[itt,badind[0]-1])
NewEOS.cs[itt,badind] = np.full(len(badind),NewEOS.cs[itt,badind[0]-1])
NewEOS.cv[itt,badind] = np.full(len(badind),NewEOS.cv[itt,badind[0]-1])
NewEOS.KPA[itt,badind] = np.full(len(badind),2)
NewEOS.MDQ[itt,badind] = np.full(len(badind),-1) # replaced tension region flag
else:
print('SOMETHING VERY WRONG WITH TENSION IN THE TABLE')
makethecodestop # please tell me a more graceful way to stop the notebook
#
# THIS SECTION RESETS NEGATIVE SPECIFIC ENTROPIES WITH ADJACENT VALUES OR MINIMUM POSITIVE VALUES
# THESE VALUES TYPICALLY DEFINE THE COLD COMPRESSION LIMIT OF THE MATERIAL
# OR SPURIOUS NEGATIVE ENTROPIES AT VERY LOW PRESSURES (IMPERFECT DEBYE MODEL IN ANEOS)
for itt in range(NewEOS.NT-1,-1,-1):
tmp = np.where(NewEOS.S[itt,:] < 0.)
if (len(tmp[0]) > 0):
badind = tmp[0]
if badind[0] > 0:
#print(itt, antarr[itt], andarr[badind[0]], badind[0],len(badind),'negative entropy', ansarr[itt,badind[0]],ansarr[itt,badind[0]-1])
NewEOS.P[itt,badind] = np.full(len(badind),NewEOS.P[itt,badind[0]-1]) # use the adjacent pressure at this temperature in the dome
NewEOS.U[itt,badind] = np.full(len(badind),NewEOS.U[itt,badind[0]-1])
NewEOS.S[itt,badind] = np.full(len(badind),NewEOS.S[itt,badind[0]-1])
NewEOS.A[itt,badind] = np.full(len(badind),NewEOS.A[itt,badind[0]-1])
NewEOS.cs[itt,badind] = np.full(len(badind),NewEOS.cs[itt,badind[0]-1])
NewEOS.cv[itt,badind] = np.full(len(badind),NewEOS.cv[itt,badind[0]-1])
#NewEOS.KPA[itt,badind] # leave as original region flag
NewEOS.MDQ[itt,badind] = np.full(len(badind),-2) # negative entropies flag
#print('Some NEGATIVE S AT THIS INDEX, TEMP(K): ',itt, NewEOS.T[itt],NewEOS.P[itt,badind[0]-1],NewEOS.P[itt,badind[0]-2]) #, badind[0],len(badind),'negative entropy', NewEOS.S[itt,badind[0]])
if badind[0] == 0:
print('All S VALUES NEGATIVE AT THIS INDEX, TEMP(K): ',itt, NewEOS.T[itt]) #, badind[0],len(badind),'negative entropy', NewEOS.S[itt,badind[0]])
NewEOS.S[itt,badind] = np.full(len(badind),1.E-10)
NewEOS.U[itt,badind] = np.full(len(badind),1.E-10) # also replace the negative sp. internal energies
NewEOS.MDQ[itt,badind] = np.full(len(badind),-2) # negative entropies flag
#### ONLY WRITE A NEW TABLE IN DEVELOPMENT MODE
if DEVMODE:
#### WRITE NEW SESAME TABLE WITH NO TENSION REGION
# WRITE STANDARD (SHORT) SESAME FILE
# WRITE SESAME TABLE TO FILE LIMITED TO P, E, HFE
NewEOS.writestdsesame(writestdsesfname="NEW-SESAME-STD-NOTENSION.TXT")
#### ONLY WRITE A NEW TABLE IN DEVELOPMENT MODE
if DEVMODE:
#### WRITE MDQ Flag as a 301-style table
NewEOS.writemdqsesame(writemdqsesfname="NEW-SESAME-MDQ.TXT")
#
#--------------------------------------------------------------------------
########## MAKE GADGET2 EOS TABLE ARRAYS ###################
# LATER WE CAN TURN THIS INTO A FUNCTION IN THE GADGET EOS OBJECT
# FLAG IS SET ABOVE IN THE USER INPUT SECTION
# MAKEGADGETTABLE = 1 # 1 - do it ; 0 - skip it
if MAKEGADGETTABLE:
print('Starting interpolation for GADGET table.')
GadEOS = extGADtable() # make new empty Gadget EOS object
#
# rho array is andarr to match the SESAME table
# S array is gridsarr
GadEOS.ND = len(gridrarr)
GadEOS.NS = len(gridsarr)
GadEOS.rho = gridrarr
GadEOS.S = gridsarr
GadEOS.P = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.T = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.U = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.A = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.cs = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.cv = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.KPA = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.MDQ = np.zeros((GadEOS.NS,GadEOS.ND))
GadEOS.MODELNAME = NewEOS.MODELNAME+'-gadget-linear-int'
#
# some combinations of density and sp. entropy are not in the EOS surface
# in these cases, apply minimum values
gadpmin = np.min(NewEOS.P) # GPa
gadsmin = 1.E-30 # MJ/K/kg
gademin = np.min(NewEOS.U) # MJ/kg
gadtmin = 1. # K
gadcmin = np.min(NewEOS.cs) # cm/s
gadcvmin = 0. # MJ/K/kg
gadamin = np.min(NewEOS.A) # can be negative # MJ/kg
print('Minimum values used in the rational function interpolation scheme:')
print('gadpmin,gadsmin,gademin,gadtmin,gadcmin,gadcvmin,gadamin=')
print(gadpmin,gadsmin,gademin,gadtmin,gadcmin,gadcvmin,gadamin)
#
# some combinations of density and sp. entropy are not in the EOS surface
# in these cases, fill the region with the adjacent real values from the original T-RHO table
# ----------------------------------------------------------
# SIMPLE LINEAR INTERPOLATION TO FLIP T-RHO to S-RHO table
print("LINEAR INTERPOLATION FOR GADGET TABLE.")
for iid in range(0,GadEOS.ND):
# same density arrays for the T-rho table and S-rho table
sall1d = NewEOS.S[:,iid]
pall1d = NewEOS.P[:,iid]
eall1d = NewEOS.U[:,iid]
tall1d = NewEOS.T[:]
call1d = NewEOS.cs[:,iid]
cvall1d = NewEOS.cv[:,iid]
aall1d = NewEOS.A[:,iid]
kall1d = NewEOS.KPA[:,iid]
mdqall1d = NewEOS.MDQ[:,iid]
# interpolate P at the new S
testinterp = interpolate.interp1d(sall1d,pall1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.P[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.P[tmpind,iid] = pall1d[NewEOS.NT-1]
# interpolate E at the new S
testinterp = interpolate.interp1d(sall1d,eall1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.U[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.U[tmpind,iid] = eall1d[NewEOS.NT-1]
# interpolate T at the new S
testinterp = interpolate.interp1d(sall1d,tall1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.T[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.T[tmpind,iid] = tall1d[NewEOS.NT-1]
# interpolate sound speed at the new S
testinterp = interpolate.interp1d(sall1d,call1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.cs[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.cs[tmpind,iid] = call1d[NewEOS.NT-1]
# interpolate sp. heat capacity at the new S
testinterp = interpolate.interp1d(sall1d,cvall1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.cv[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.cv[tmpind,iid] = call1d[NewEOS.NT-1]
# interpolate HFE at the new S
testinterp = interpolate.interp1d(sall1d,aall1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.A[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.A[tmpind,iid] = call1d[NewEOS.NT-1]
# interpolate phase information KPA flag at the new S
testinterp = interpolate.interp1d(sall1d,kall1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.KPA[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.KPA[tmpind,iid] = call1d[NewEOS.NT-1]
# interpolate model development quality flag at the new S
testinterp = interpolate.interp1d(sall1d,mdqall1d)
tmpind = np.where(gridsarr < np.max(sall1d))[0]
GadEOS.MDQ[tmpind,iid] = testinterp(gridsarr[tmpind])
tmpind = np.where(gridsarr >= np.max(sall1d))[0]
GadEOS.MDQ[tmpind,iid] = call1d[NewEOS.NT-1]
#
GadEOSlin = deepcopy(GadEOS)
#
'''
# ----------------------------------------------------------
# 1D RATIONAL FUNCTION INTERPOLATION METHOD FROM KERLEY
print("RATIONAL FUNCTION INTERPOLATION TO GENERATE GADGET2 EOS TABLE.")
for iid in range(0,GadEOS.ND):
GadEOS.MODELNAME = NewEOS.MODELNAME+'-gadget-ratfunc-int'
#
# same density arrays for the T-rho table and S-rho table
sall1d = NewEOS.S[:,iid]
pall1d = NewEOS.P[:,iid]
eall1d = NewEOS.U[:,iid]
tall1d = NewEOS.T[:]
call1d = NewEOS.cs[:,iid]
cvall1d = NewEOS.cv[:,iid]
aall1d = NewEOS.A[:,iid]
#kall1d = NewEOS.KPA[:,iid]
#mdqall1d = NewEOS.MDQ[:,iid]
#
# interpolate P at the new S
GadEOS.P[:,iid] = rf1d(sall1d,pall1d,gridsarr,gadpmin)
# interpolate E at the new S
GadEOS.U[:,iid] = rf1d(sall1d,eall1d,gridsarr,gademin)
# interpolate T at the new S
GadEOS.T[:,iid] = rf1d(sall1d,tall1d,gridsarr,gadtmin)
# interpolate sound speed at the new S
GadEOS.cs[:,iid] = rf1d(sall1d,call1d,gridsarr,gadcmin)
# interpolate sp. heat capacity at the new S
GadEOS.cv[:,iid] = rf1d(sall1d,cvall1d,gridsarr,gadcvmin)
# interpolate HFE at the new S
GadEOS.A[:,iid] = rf1d(sall1d,aall1d,gridsarr,gadamin)
# Do not interpolate KPA or MDQ with rational function interp. Use Linear.
# do not overwrite the linear interpolation above.
'''
#
print('Done interpolating the gadget2 table.')
#print('Using RATIONAL FUNCTION INTERPOLATION EXCEPT FOR KPA and MDQ FLAGS (bilinear).')
if DEVMODE:
# ONLY WRITE GADGET2 TABLE TO DISK IN DEVELOPMENT MODE
#### WRITE NEW GADGET2 TABLE WITH NO TENSION REGION
#### This ascii table format follows the sesame table format of 5 columns of numbers in 16.8e format
#### the STYLE variable is just a counter to 5 to know when to write a newline
GadEOS.writestdgadget(writestdgadgetfname="NEW-GADGET-STD-NOTENSION.TXT")
GadEOS.writeextgadget(writeextgadgetfname="NEW-GADGET-EXT-NOTENSION.TXT")
In [ ]:
In [10]:
# READ IN FORSTERITE MATERIAL DATA SETS
datadir='data/'
#======================================================================
#======================================================================
# Gather some experimental and theoretical data on forsterite
FoSTP_S = 0.6689E-3 # MJ/K/kg STP is 0.6689 kJ/K/kg (Robie et al. 1982)
# Read in 1 bar data for forsterite from Gillet et al. 1991
#T_solid (K), S_solid (J/K/kg), T_melt (K), S_melt (J/K/kg)
# **** Melt is calculated sp. entropy based on constant Cv from Thomas et al. 2013 ****
Gilletfile=datadir+'Gillet-1991-Forsterite_Entropy_to_3000K.txt'
Gilletdatarr = pd.read_csv(Gilletfile,skiprows=1)
# Read in data thief'd melt curve for forsterite from Mosenfelder et al. 2007
# P GPa and T K
# Asimow acknowledges that this is not a well constrained curve May 2019
Mosenfelderfile=datadir+'Mosenfelder-2007-melt-curve.txt'
Mosenfelderdatarr = pd.read_csv(Mosenfelderfile,skiprows=1)
# Gruneisen parameter for liquid forsterite from Z release data
# Erik J. Davies, et al., 2019, IN PREPARATION FOR PUBLICATION
# Gamma, G_e, Density, rho_e , q, q_e rho in kg/m3
fileZdata=datadir+'Davies-2019-Gamma_Release_Data_20190812.txt'
#Load in Shallow Release Densities and Gammas
SR_rho=np.loadtxt(fileZdata,delimiter=',',skiprows=1,usecols=[2])/1.e3 # g/cm3
SR_rho_e=np.loadtxt(fileZdata,delimiter=',',skiprows=1,usecols=[3])/1.e3 # g/cm3
SR_gamma=np.loadtxt(fileZdata,delimiter=',',skiprows=1,usecols=[0])
SR_gamma_e=np.loadtxt(fileZdata,delimiter=',',skiprows=1,usecols=[1])
# Root et al. 2018, QMD Hugoniot including specific heat capacities calculated by Townsend
fileQMDHUGdata=datadir+'Root-2018-Forsterite-QMD-Hugoniot.txt'
# QMD values with no near-STP point (skip 3)
QMDH_r1=np.loadtxt(fileQMDHUGdata,skiprows=3,usecols=[0]) # g/cm3
QMDH_cv=np.loadtxt(fileQMDHUGdata,skiprows=3,usecols=[5])/1.e3 # MJ/K/kg
QMDH_grun=np.loadtxt(fileQMDHUGdata,skiprows=3,usecols=[4]) # Gruneisen Parameter
QMDH_up=np.loadtxt(fileQMDHUGdata,skiprows=3,usecols=[6]) # km/s
QMDH_us=np.loadtxt(fileQMDHUGdata,skiprows=3,usecols=[7]) # km/s
# QMD Hugoniot Points with near-STP point (skip 2)
QMDH_r=np.loadtxt(fileQMDHUGdata,skiprows=2,usecols=[0]) # g/cm3
QMDH_e=np.loadtxt(fileQMDHUGdata,skiprows=2,usecols=[1]) # MJ/kg
QMDH_p=np.loadtxt(fileQMDHUGdata,skiprows=2,usecols=[2]) # GPa
QMDH_t=np.loadtxt(fileQMDHUGdata,skiprows=2,usecols=[3]) # K
# Root et al. 2018 Z Machine All PV Hugoniot data points
zhugoniotfile = open(datadir+"Root-2018-ForsteriteHugoniotData-03Nov2017.txt","r") # SESAME units
Zdat_all=np.loadtxt(zhugoniotfile,skiprows=2,usecols=[4,5,6,7,8,9,10,11])
zhugoniotfile.close()
Zdat_up=Zdat_all[:,0]# km/s
Zdat_uperr=Zdat_all[:,1] # km/s
Zdat_us=Zdat_all[:,2] # km/s
Zdat_userr=Zdat_all[:,3] # km/s
Zdat_r=Zdat_all[:,4] # g/cm3
Zdat_rerr=Zdat_all[:,5] # g/cm3
Zdat_p=Zdat_all[:,6] # GPa
Zdat_perr=Zdat_all[:,7] # GPa
# Root et al. 2018 Z Machine All PVT Hugoniot data points
# One point corrected; one point added in Davies et al. 2019
#P (Gpa),Pe,T (K),Te,Us (km/s),Use,Up,Upe,Flyer V
zhugoniotfile = open(datadir+"Root-2018-Davies-2019-Forsterite_PT_hugDat.csv","r") # SESAME units
ZTdat_all=np.loadtxt(zhugoniotfile,skiprows=3,usecols=[0,1,2,3,4,5,6,7],delimiter=',')
zhugoniotfile.close()
ZTdat_p=ZTdat_all[:,0] # GPa
ZTdat_perr=ZTdat_all[:,1] # GPa
ZTdat_t=ZTdat_all[:,2] # K
ZTdat_terr=ZTdat_all[:,3] # K
ZTdat_us=ZTdat_all[:,4] # km/s
ZTdat_userr=ZTdat_all[:,5] # km/s
ZTdat_up=ZTdat_all[:,6]# km/s
ZTdat_uperr=ZTdat_all[:,7] # km/s
#ZTdat_r= # g/cm3
#ZTdat_rerr= # g/cm3
# Root et al. 2018 FITTED WITH PROPAGATED ERRORS PVT Hugoniot with Sp. Entropies from Davies et al. 2019
#P (Pa), T (K), S (J/K/kg), rho (kg/m^3), Pe, Te, Se, rho_e
zhugoniotfile = open(datadir+"Davies-2019-Z_Hugoniot-20190922.txt","r") # mks
zhugfitarr = pd.read_csv(zhugoniotfile,skiprows=1) # only validated bewteen about 220 and 950 GPa
zhugoniotfile.close()
Zfit_r0 = 3.22 # g/cm3
Zfit_p = zhugfitarr.iloc[:,0].values/1.E9 # GPa
Zfit_perr = zhugfitarr.iloc[:,4].values/1.E9 # GPa
Zfit_t = zhugfitarr.iloc[:,1].values # K
Zfit_terr = zhugfitarr.iloc[:,5].values # K
Zfit_s = zhugfitarr.iloc[:,2].values/1.E6 # MJ/K/kg
Zfit_serr = zhugfitarr.iloc[:,6].values/1.E6 # MJ/K/kg
Zfit_r = zhugfitarr.iloc[:,3].values/1.E3 # g/cm3
Zfit_rerr = zhugfitarr.iloc[:,7].values/1.E3 # g/cm3
Zfit_up = np.sqrt((Zfit_p)*(1./Zfit_r0-1./Zfit_r)) # km/s
Zfit_us = (1./Zfit_r0)*np.sqrt((Zfit_p)/(1./Zfit_r0-1./Zfit_r)) # km/s
# Davies et al. 2019
# Entropy tie point ('point E') on the Fo principal Hugoniot
Ztie_p=237. # GPa
Ztie_perr=83. # GPa
Ztie_s=4036.E-6 # MJ/K/kg
Ztie_serr=212.E-6 # MJ/K/kg
# Root et al. 2018 OMEGA decaying shock temperature data
#OMEGA Livermore data 77780
OM_rhoD=3277 #Need for livermore data, kg/m^3
OM_rhoDe=OM_rhoD*0.003
fname=datadir+'Root-2018-s77775_withP.txt'
OM_DU1=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[0])
OM_DUe1=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[1])
OM_DR1=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[4])
OM_DRe1=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[5])
OM_DT1=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[2])
OM_DTe1=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[3])
OM_D1P=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[6])
OM_D1Pe=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[7])
fname=datadir+'Root-2018-s77776_withP.txt'
OM_DU2=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[0])
OM_DUe2=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[1])
OM_DR2=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[4])
OM_DRe2=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[5])
OM_DT2=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[2])
OM_DTe2=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[3])
OM_D2P=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[6])
OM_D2Pe=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[7])
fname=datadir+'Root-2018-s77779_withP.txt'
OM_DU3=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[0])
OM_DUe3=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[1])
OM_DR3=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[4])
OM_DRe3=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[5])
OM_DT3=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[2])
OM_DTe3=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[3])
OM_D3P=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[6])
OM_D3Pe=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[7])
fname=datadir+'Root-2018-s77780_withP.txt'
OM_DU4=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[0])
OM_DUe4=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[1])
OM_DR4=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[4])
OM_DRe4=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[5])
OM_DT4=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[2])
OM_DTe4=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[3])
OM_D4P=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[6])
OM_D4Pe=np.loadtxt(fname,delimiter=',',skiprows=1,usecols=[7])
# low pressure gas gun Hugoniot data datathiefed from Mosenfelder et al. 2007
lowhugoniotfile = open(datadir+"Mosenfelder-2007-forsterite-hugoniot.txt","r") # density g/cm3, pressure GPa
lowhugdatarr = pd.read_csv(lowhugoniotfile,skiprows=1)
lowhugoniotfile.close()
LowHugDat_r0 = 3.22 # g/cm3
LowHugDat_r = lowhugdatarr.iloc[:,0].values # g/cm3
LowHugDat_p = lowhugdatarr.iloc[:,1].values # GPa
LowHugDat_up = np.sqrt((LowHugDat_p)*(1./LowHugDat_r0-1./LowHugDat_r)) # km/s
LowHugDat_us = (1./LowHugDat_r0)*np.sqrt((LowHugDat_p)/(1./LowHugDat_r0-1./LowHugDat_r)) # km/s
#print(LowHugDat_up)
#print(LowHugDat_us)
# Fiquet et al 2010 Peridotite solidus and liquidus
# P GPa, T K
peridotitefile = open(datadir+"Fiquet-2010-Science-Peridotite-Melting-Fig3-solidus.txt","r")
peridotitesolidusdatarr = pd.read_csv(peridotitefile,skiprows=1)
peridotitefile.close()
peridotitefile = open(datadir+"Fiquet-2010-Science-Peridotite-Melting-Fig3-liquidus.txt","r")
peridotiteliquidusdatarr = pd.read_csv(peridotitefile,skiprows=1)
peridotitefile.close()
# Thomas & Asimow 2013 Forsterite Liquid shock data BAD TABULATED VALUES
#foliqhugpres = [0.,9.21,22.98,47.6,75.0,96.7,114.3]
#foliqhugdens = [2.273,3.34,3.74,4.1,4.29,4.68,4.68] # Tabulated incorrect values
# recalculate the TA13 Hugoniot Points
# May 2019: Confirmed with Asimow that the tabulated values are incorrect and recalculation values are correct
# He says incorrect values only in the published tables; Correct values used in the thermodynamic analysis.
foliqrho0 = 2597. # kg/m3
foliqup = np.asarray([1.644,0.886,4.08,2.59,3.41,4.43]) # km/s
foliqus = np.asarray([5.38,4.,9.14,7.1,8.47,9.95]) # km/s
foliqup = foliqup*1000. # m/s
foliqus = foliqus*1000. # m/s
foliqp = foliqrho0*foliqup*foliqus # Pa calculate correct liquid Hugoniot values
foliqv = (1./foliqrho0)*(1.-foliqup/foliqus) # m3/kg calculate correct liquid Hugoniot values
foliqrho = 1./foliqv # kg/m3
# convert to SESAME units
foliq_r = foliqrho/1.E3 # g/cm3
foliq_r0 = foliqrho0/1.E3 # g/cm3
foliq_up = foliqup/1.E3 # km/s
foliq_us = foliqus/1.E3 # km/s
foliq_p = foliqp/1.E9 # GPa
foliq_t0 = 2273. # K
Color mesh plots of the SESAME Rho-T table¶
In [11]:
# PLOT COLOR SHADED VALUES RHO-T TABLE
lw=1
sfont = 15
ds = (10,10)
%matplotlib inline
fig, ([ax0, ax1], [ax2,ax3], [ax4,ax5])= plt.subplots(nrows=3,ncols=2,figsize=(14,24))
plt.subplots_adjust(wspace=0.4)
#plt.tight_layout(pad=0.6)
##================ Pressure
im1=ax0.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.P)+25)/29.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax0.plot(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax0.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax0.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.set_ylim(0.,20000)
ax0.set_xlim(0,30.)
ax0.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax0.set_ylabel('Temperature (K)',size=sfont)
ax0.set_title('Colors=log$_{10}$(P (GPa))',size=sfont)
ax0.tick_params(labelsize=sfont)
divider0 = make_axes_locatable(ax0)
cax0 = divider0.append_axes('right', size='5%', pad=0.05)
cbar0 = fig.colorbar(im1, cax=cax0, ticks = [],orientation='vertical')
#cbar0.ax.set_yticklabels([' ',' ',' ']) # vertical colorbar
cbar0.set_label('Log$_{10}$(P) [GPa]',size=sfont)
#cbar0.ax.set_yticklabels(['-25','-11','+4']) # vertical colorbar
im1=ax1.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.P)+25)/29.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax1.loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.loglog(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.loglog(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax1.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax1.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.set_ylim(10.,1.E7)
ax1.set_xlim(1.E-21,100.)
ax1.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax1.set_ylabel('Temperature (K)',size=sfont)
ax1.set_title('Colors=log$_{10}$(P (GPa))',size=sfont)
ax1.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax1)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-25','-11', '+4']) # vertical colorbar
cbar.set_label('Log$_{10}$(P) [GPa]',size=sfont)
#================ Sp. Int. Energy
im1=ax2.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.U)+4.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax2.plot(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax2.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax2.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.set_ylim(0.,20000)
ax2.set_xlim(0,30.)
ax2.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax2.set_ylabel('Temperature (K)',size=sfont)
ax2.set_title('Colors=log$_{10}$(Sp. Int. Energy (MJ/kg))',size=sfont)
ax2.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax2)
cax = divider.append_axes('right', size='5%', pad=0.05)
# does not want to label ticks in this location
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['','','']) # vertical colorbar
cbar.set_label('Log$_{10}$(E) [MJ/kg]',size=sfont)
#cbar.ax.set_yticklabels(['-4','+1','+6']) # vertical colorbar
ax3.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.U)+4.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax3.loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax3.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax3.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.set_ylim(10.,1.E7)
ax3.set_xlim(1.E-21,100.)
ax3.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax3.set_ylabel('Temperature (K)',size=sfont)
ax3.set_title('Colors=log$_{10}$(E (MJ/kg))',size=sfont)
ax3.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax3)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-4', '+1','+6']) # vertical colorbar
cbar.set_label('Log$_{10}$(E) [MJ/kg]',size=sfont)
#================ Sp. Entropy
im1=ax4.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.S)+4.)/4.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax4.plot(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax4.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax4.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.set_ylim(0.,20000)
ax4.set_xlim(0,30.)
ax4.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax4.set_ylabel('Temperature (K)',size=sfont)
ax4.set_title('Colors=log$_{10}$(Sp. Entropy (MJ/K/kg))',size=sfont)
ax4.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax4)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['-4', '-2', '0']) # vertical colorbar
cbar.set_label('Log$_{10}$(S) [MJ/K/kg]',size=sfont)
ax5.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.S)+4.)/4.,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax5.loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax5.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax5.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.set_ylim(10.,1.E7)
ax5.set_xlim(1.E-21,100.)
ax5.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax5.set_ylabel('Temperature (K)',size=sfont)
ax5.set_title('Colors=log$_{10}$(Sp. Entropy (MJ/K/kg))',size=sfont)
ax5.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax5)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-4', '-2','0']) # vertical colorbar
cbar.set_label('Log$_{10}$(S) [MJ/K/kg]',size=sfont)
##============= start new plot
fig2, ([ax0, ax1], [ax2,ax3], [ax4,ax5])= plt.subplots(nrows=3,ncols=2,figsize=(14,24))
plt.subplots_adjust(wspace=0.4)
#================ Sound Speed
im1=ax0.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.cs)+3.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax0.plot(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax0.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax0.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.set_ylim(0.,20000)
ax0.set_xlim(0,30.)
ax0.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax0.set_ylabel('Temperature (K)',size=sfont)
ax0.set_title('Colors=log$_{10}$(Sound Speed (cm/s))',size=sfont)
ax0.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax0)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['-3', '+2', '+7']) # vertical colorbar
cbar.set_label('Log$_{10}$(Cs) [cm/s]',size=sfont)
ax1.pcolormesh(NewEOS.rho,NewEOS.T,(np.log10(NewEOS.cs)+3.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax1.loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.loglog(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.loglog(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax1.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax1.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.set_ylim(10.,1.E7)
ax1.set_xlim(1.E-21,100.)
ax1.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax1.set_ylabel('Temperature (K)',size=sfont)
ax1.set_title('Colors=log$_{10}$(sound speed (cm/s))',size=sfont)
ax1.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax1)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-3', '+2', '+7']) # vertical colorbar
cbar.set_label('Log$_{10}$(Cs) [cm/s]',size=sfont)
#================ HFE
amin = np.min(NewEOS.A)
amin = -1000.
alogmax = 1500. #np.max(anaarrodd)-amin #np.max(np.log10(anaarrodd-amin))
#print('amin, log10(amin)',amin,np.log10(-amin))
#print('alogmax=',alogmax)
im1=ax2.pcolormesh(NewEOS.rho,NewEOS.T,(NewEOS.A-amin)/alogmax,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax2.plot(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax2.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax2.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.set_ylim(0.,20000)
ax2.set_xlim(0,30.)
ax2.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax2.set_ylabel('Temperature (K)',size=sfont)
ax2.set_title('Colors=HFE (MJ/kg)',size=sfont)
ax2.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax2)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['-1000','-500','0','500']) # vertical colorbar
cbar.set_label('Log$_{10}$(HFE) [MJ/kg]',size=sfont)
ax3.pcolormesh(NewEOS.rho,NewEOS.T,(NewEOS.A-amin)/alogmax,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax3.loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax3.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax3.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.set_ylim(10.,1.E7)
ax3.set_xlim(1.E-21,100.)
ax3.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax3.set_ylabel('Temperature (K)',size=sfont)
ax3.set_title('Colors=HFE (MJ/kg)',size=sfont)
ax3.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax3)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0,.333,.6667, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-1000','-500','0','500']) # vertical colorbar
cbar.set_label('Log$_{10}$(HFE) [MJ/kg]',size=sfont)
#================ KPA flag
cmap2 = cm.get_cmap('plasma', 6) # 6 discrete colors
im1=ax4.pcolormesh(NewEOS.rho,NewEOS.T,((NewEOS.KPA)-0.5)/6.,cmap=cmap2,vmin=0,vmax=1,edgecolors='face')
#im1=ax4.pcolormesh(NewEOS.rho,NewEOS.T,((NewEOS.KPA))/6.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax4.plot(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax4.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax4.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.set_ylim(0.,20000)
ax4.set_xlim(0,30.)
ax4.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax4.set_ylabel('Temperature (K)',size=sfont)
ax4.set_title('Colors=KPA flag',size=sfont)
ax4.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax4)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['0','1','2','3','4','5', '6']) # vertical colorbar
cbar.set_label('KPA Flag',size=sfont)
ax5.pcolormesh(NewEOS.rho,NewEOS.T,((NewEOS.KPA)-0.5)/6.,cmap=cmap2,vmin=0,vmax=1)
ax5.loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax5.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax5.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.set_ylim(10.,1.E7)
ax5.set_xlim(1.E-21,100.)
ax5.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax5.set_ylabel('Temperature (K)',size=sfont)
ax5.set_title('Colors=KPA flag',size=sfont)
ax5.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax5)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = np.arange(13)/12, orientation='vertical')
cbar.ax.set_yticklabels(['','1','','2','','3','','4','','5','', '6']) # vertical colorbar
cbar.set_label('KPA Flag',size=sfont)
fig2.show()
Model Data Quality (MDQ) Flag¶
We provide an MDQ rating which is saved as a 301-style SESAME table. The MDQ rating is a qualitative guide for users that provides some known quality control information. This information is necessarily subjective and incomplete. The rating does not guarantee any fidelity in the EOS model except for points that have been directly compared to experimental data in the plots below.
- MDQ=1: Data point has experimental data and falls within experimental error. NOT USED AT THIS TIME. Will be added in the future.
- MDQ=0: Data point rating is neutral. The value appears to be a thermodynamically self-consistent model point without known gross errors.
- MDQ=-1: Data point rating is erroneous. The value is not thermodynamically correct in a known way. In this work, this flag is used for the replacement values for the tension region to generate an all positive pressure equilibrium EOS table. The current replacement scheme is to use the values in the adjacent grid cell: for each P and T in the sublimation region, use values at the adjacent density with positive pressure. The magnitude of the error is small, but the derivatives in this region will be incorrect.
- MDQ=-2: Data point rating is non-physical. The value is not thermodynamically correct in a known way. In this work, this flag is used for ANEOS output with negative values for the specific entropy.
- MDQ=-4: Developer judgement that this region of phase space does not provide a robust representation of the material. There are no high-pressure solid phases in this EOS model. Seek alternative models for problems focused in this region.
- MDQ=-5: Developer judgement that this region of phase space does not provide a robust representation of the material. Applied to regions with pressures > 1 TPa. The Gruneisen gamma value is too large for liquid in this region and missing physics at higher pressures and temperatures. Seek alternative models for problems focused in this region.
In [12]:
# check the user-defined model data quality flag across the EOS surface
uniqmdqarr = np.unique(NewEOS.MDQ)
print("Unique values in the MDQ flag array:", uniqmdqarr)
print("Value: # elements with this value")
#get_indexes = lambda x, xs: [i for (y, i) in zip(xs, range(len(xs))) if x == y]
for i in uniqmdqarr:
ix = get_indexes(i,np.reshape(NewEOS.MDQ,NewEOS.ND*NewEOS.NT))
print(i,': ',len(ix))
##============= start new plot
fig3, ([ax4, ax5])= plt.subplots(nrows=1,ncols=2,figsize=(14,8))
plt.subplots_adjust(wspace=0.4)
#================ MDQ flag
cmap2 = cm.get_cmap('plasma', 6) # 6 discrete colors
#im1=ax4.pcolormesh(NewEOS.rho,NewEOS.T,((NewEOS.MDQ)+5)/6.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
im1=ax4.pcolormesh(NewEOS.rho,NewEOS.T,((NewEOS.MDQ)+5)/6.,cmap=cmap2,vmin=0,vmax=1,edgecolors='face')
ax4.plot(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax4.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax4.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.set_ylim(0.,20000)
ax4.set_xlim(0,30.)
ax4.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax4.set_ylabel('Temperature (K)',size=sfont)
ax4.set_title('Colors=MDQ flag',size=sfont)
ax4.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax4)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['','-5','','-4','','-3','','-2','','-1','','0','','1']) # vertical colorbar
cmap2 = cm.get_cmap('plasma', 6) # 6 discrete colors
ax5.pcolormesh(NewEOS.rho,NewEOS.T,((NewEOS.MDQ)+5)/6.,cmap=cmap2,vmin=0,vmax=1)
#ax5.pcolormesh(NewEOS.rho,NewEOS.T,((NewEOS.MDQ)+5)/6.,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax5.loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rv,NewEOS.vc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rl[0],NewEOS.vc.T[0],'ko')
if NewEOS.mc.NT > 0:
ax5.plot(NewEOS.mc.rl,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax5.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.set_ylim(10.,1.E7)
ax5.set_xlim(1.E-21,100.)
ax5.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax5.set_ylabel('Temperature (K)',size=sfont)
ax5.set_title('Colors=MDQ flag',size=sfont)
ax5.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax5)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = np.arange(13)/12, orientation='vertical')
cbar.ax.set_yticklabels(['','-5','','-4','','-3','','-2','','-1','','0','','1']) # vertical colorbar
fig3.show()
In [ ]:
ANEOS Hugoniot Compared to Experimental Data¶
The following plots compare the ANEOS model Hugoniots with laboratory data and ab initio calculations. Shock Hugoniot data points from gas gun experiments are summarized in Figure 1 of Mosenfelder et al. 2007. High pressure Hugoniot points obtained by the Z machine and QMD calculations are from Root et al. 2018.
Entropy on the Hugoniot derived by Davies et al., 2019, using the Z Hugoniot, Z-derived Gruneisen parameters, and thermodynamic integration.
Orange points are corrected data points for the liquid (rho=2.661 g/cm$^3$, T$_0$=2273 K) forsterite Hugoniot from Thomas and Asimow 2013.
ANEOS STP Hugoniots: red -- calculated in the ANEOS code; blue -- calculated by linear interpolation of the EOS table.
In [ ]:
In [13]:
# Display the initial conditions for the Hugoniot in ANEOS.OUTPUT
print('\nRequested ANEOS Hugoniot initial state from (THUG,RHUG) (red curves in plots below):')
print('Initial Pressure (GPa):',NewEOS.anhug.P[0])
print('Initial Temperature (K):',NewEOS.anhug.T[0])
print('Initial Sp. Entropy (MJ/K/kg):',NewEOS.anhug.S[0])
print('Initial Sp. Internal Energy (MJ/kg):',NewEOS.anhug.U[0])
print('Initial Density (g/cm3):',NewEOS.anhug.rho[0])
#
#========== PLOTTING STYLES FOR LOTS OF PLOTS =================
styleqmd = ['^','red',5,'QMD calc (Root et al. 2018)']
stylezdat = ['^','black',5,'Z data (Root et al. 2018)']
stylegg = ['+','green',5,'Gas gun data\n(Mosenfelder et al. 2007)']
styleliq = ['^','orange',7,'Liquid Fo data corrected\n(Thomas & Asimow 2013)']
styleliqhug = ['-','orange',1,'ANEOS Liquid Fo Hugoniot']
stylezfit = ['-','green',1,'Z fit (Davies et al. 2019)']
styleanhug = ['-','red',1,'ANEOS Hugoniot']
stylestphug = ['-','blue',1,'Tabulated STP Hugoniot']
styleanphase = ['-','black',1,'ANEOS Phase Boundaries']
stylephasept = ['o','black',6]
#======================LOTS OF PLOTS============================
# plot the Hugoniots for comparison
sfont = 15
fig, axes = plt.subplots(nrows=3, ncols=2, figsize=(14,18))
plt.subplots_adjust(wspace=0.4)
#-------------
# Pressure-Density Data vs. ANEOS
ai=0
aj=0
axes[ai,aj].plot(QMDH_r[1::],QMDH_p[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].plot(Zdat_r,Zdat_p,stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3])
axes[ai,aj].plot(LowHugDat_r,LowHugDat_p,stylegg[0],markersize=stylegg[2],color=stylegg[1],label=stylegg[3])
axes[ai,aj].plot(Zfit_r,Zfit_p,stylezfit[0],linewidth=stylezfit[2],color=stylezfit[1],label=stylezfit[3])
axes[ai,aj].plot(NewEOS.anhug.rho,NewEOS.anhug.P,styleanhug[0],linewidth=styleanhug[2],color=styleanhug[1],label=styleanhug[3])
axes[ai,aj].plot(NewEOS.hug.rho,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].set_ylim(0,1200)
axes[ai,aj].set_xlim(3.,8.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].legend(fontsize=sfont-5)
#-------------
# Pressure - Temperature Data vs. ANEOS
ai=0
aj=1
#####OMEGA data from Root et al. 2018
col=local_cmaps.parula(0.5)
axes[ai,aj].fill_between(OM_D1P*1000,(OM_DT1-OM_DTe1)/1000,(OM_DT1+OM_DTe1)/1000,label="OMEGA data (Root et al. 2018)",
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D2P*1000,(OM_DT2-OM_DTe2)/1000,(OM_DT2+OM_DTe2)/1000,
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D3P*1000,(OM_DT3-OM_DTe3)/1000,(OM_DT3+OM_DTe3)/1000,
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D4P*1000,(OM_DT4-OM_DTe4)/1000,(OM_DT4+OM_DTe4)/1000,
color=col,alpha=0.25)
axes[ai,aj].plot(QMDH_p[1::],QMDH_t[1::]/1.E3,styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].errorbar(ZTdat_p,ZTdat_t/1.E3,xerr=ZTdat_perr,yerr=ZTdat_terr/1.E3,fmt=stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3],elinewidth=1)
axes[ai,aj].plot(Zfit_p,Zfit_t/1.E3,stylezfit[0],linewidth=stylezfit[2],color=stylezfit[1],label=stylezfit[3])
axes[ai,aj].plot(NewEOS.anhug.P,NewEOS.anhug.T/1.E3,styleanhug[0],linewidth=styleanhug[2],color=styleanhug[1],label=styleanhug[3])
axes[ai,aj].plot(NewEOS.hug.P,NewEOS.hug.T/1.E3,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].set_xlim(0,1200)
axes[ai,aj].set_ylim(0,50)
axes[ai,aj].set_ylabel('Temperature (1000 K)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].legend(fontsize=sfont-5)
#-------------
# Particle Velocity vs. Shock Velocity; Data vs. ANEOS
ai=1
aj=0
axes[ai,aj].plot(QMDH_up[1::],QMDH_us[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].errorbar(Zdat_up,Zdat_us,xerr=Zdat_uperr,yerr=Zdat_userr,fmt=stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3],elinewidth=1)
axes[ai,aj].plot(LowHugDat_up,LowHugDat_us,stylegg[0],markersize=stylegg[2],color=stylegg[1],label=stylegg[3])
axes[ai,aj].plot(Zfit_up,Zfit_us,stylezfit[0],linewidth=stylezfit[2],color=stylezfit[1],label=stylezfit[3])
axes[ai,aj].plot(NewEOS.anhug.up,NewEOS.anhug.us,styleanhug[0],linewidth=styleanhug[2],color=styleanhug[1],label=styleanhug[3])
axes[ai,aj].plot(NewEOS.hug.up,NewEOS.hug.us,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(foliq_up,foliq_us,styleliq[0],markersize=styleliq[2],color=styleliq[1],label=styleliq[3])
# ANEOS LIQUID HUGONIOT
# Calculate the model Hugoniot with the same initial state as Thomas & Asimow 2013
NewEOS.calchugoniot(r0=foliq_r0,t0=foliq_t0)
axes[ai,aj].plot(NewEOS.hug.up,NewEOS.hug.us,styleliqhug[0],linewidth=styleliqhug[2],color=styleliqhug[1],label=styleliqhug[3])
# Put the STP hugoniot back into the structure
NewEOS.calchugoniot(r0=NewEOS.R0REF,t0=NewEOS.T0REF)
axes[ai,aj].set_xlim(0,15)
axes[ai,aj].set_ylim(0,25)
axes[ai,aj].set_xlabel('Particle Velocity (km/s)',size=sfont)
axes[ai,aj].set_ylabel('Shock Velocity (km/s)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].legend(fontsize=sfont-5)
#-------------
# Sp. Entropy vs Pressure; Calculated from experiments vs. ANEOS
ai=1
aj=1
axes[ai,aj].plot(Zfit_p,Zfit_s*1.E3,stylezfit[0],linewidth=stylezfit[2],color=stylezfit[1],label=stylezfit[3])
axes[ai,aj].fill_between(Zfit_p,(Zfit_s-Zfit_serr)*1000.,(Zfit_s+Zfit_serr)*1000.,color=stylezfit[1],alpha=0.2)
# pressure error envelope is tiny and can't be seen on this scale
#axes[ai,aj].fill_betweenx(Zfit_s*1000.,(Zfit_p-Zfit_perr),(Zfit_p+Zfit_perr),color='red',alpha=0.2)
axes[ai,aj].plot(NewEOS.anhug.P,NewEOS.anhug.S*1.E3,styleanhug[0],linewidth=styleanhug[2],color=styleanhug[1],label=styleanhug[3])
axes[ai,aj].plot(NewEOS.hug.P,NewEOS.hug.S*1.E3,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
# Tie point from Davies et al. 2019
axes[ai,aj].errorbar(Ztie_p,Ztie_s*1.E3,xerr=Ztie_perr,yerr=Ztie_serr*1.E3,fmt='o',markersize=5,color='red',label='Entropy Tie Point (Davies et al. 2019)',elinewidth=3)
# Fo at STP from Robie et al. 1982
axes[ai,aj].plot(1.E-4,FoSTP_S*1.E3,'s',markersize=5,color='orange',label='STP (Robie et al. 1982)')
axes[ai,aj].set_ylim(0,8.)
axes[ai,aj].set_xlim(0,1200)
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].legend(fontsize=sfont-5)
#-------------
# Pressure-Density Data vs. ANEOS LOW PRESSURE + LIQUID HUGONIOT
ai=2
aj=0
#axes[ai,aj].plot(QMDH_r[1::],QMDH_p[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
#axes[ai,aj].plot(Zdat_r,Zdat_p,stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3])
axes[ai,aj].plot(LowHugDat_r,LowHugDat_p,stylegg[0],markersize=stylegg[2],color=stylegg[1],label=stylegg[3])
# Liquid forsterite Hugoniot Data
axes[ai,aj].plot(foliq_r,foliq_p,styleliq[0],markersize=styleliq[2],color=styleliq[1],label=styleliq[3])
axes[ai,aj].plot(foliq_r0,0,styleliq[0],markersize=styleliq[2],color=styleliq[1])
#axes[ai,aj].plot(Zfit_r,Zfit_p,stylezfit[0],linewidth=stylezfit[2],color=stylezfit[1],label=stylezfit[3])
# ANEOS REFERENCE POINT (STP) Hugoniots
axes[ai,aj].plot(NewEOS.anhug.rho,NewEOS.anhug.P,styleanhug[0],linewidth=styleanhug[2],color=styleanhug[1],label=styleanhug[3])
axes[ai,aj].plot(NewEOS.hug.rho,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
# ANEOS LIQUID HUGONIOT
# Calculate the model Hugoniot with the same initial state as Thomas & Asimow 2013
NewEOS.calchugoniot(r0=foliq_r0,t0=foliq_t0)
axes[ai,aj].plot(NewEOS.hug.rho,NewEOS.hug.P,styleliqhug[0],linewidth=styleliqhug[2],color=styleliqhug[1],label=styleliqhug[3])
# Put the STP hugoniot back into the structure
NewEOS.calchugoniot(r0=NewEOS.R0REF,t0=NewEOS.T0REF)
axes[ai,aj].set_ylim(-5,200)
axes[ai,aj].set_xlim(2.5,6.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].legend(fontsize=sfont-5)
#-------------
# Pressure-Density Data vs. ANEOS EXTRAPOLATED HIGH PRESSURE
ai=2
aj=1
axes[ai,aj].plot(QMDH_r[1::],QMDH_p[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].plot(Zdat_r,Zdat_p,stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3])
axes[ai,aj].plot(LowHugDat_r,LowHugDat_p,stylegg[0],markersize=stylegg[2],color=stylegg[1],label=stylegg[3])
axes[ai,aj].plot(Zfit_r,Zfit_p,stylezfit[0],linewidth=stylezfit[2],color=stylezfit[1],label=stylezfit[3])
axes[ai,aj].plot(NewEOS.anhug.rho,NewEOS.anhug.P,styleanhug[0],linewidth=styleanhug[2],color=styleanhug[1],label=styleanhug[3])
axes[ai,aj].plot(NewEOS.hug.rho,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
# Extrapolate the exponential form Hugoniot from Root et al. 2018
uptmp = NewEOS.hug.up #up in km/s
ustmp = 6.89+1.22*uptmp-1.50*uptmp*np.exp(-0.4*uptmp) # root 2018 exponential fit
ptmp = 3220*uptmp*ustmp/1.e3 # GPa
vtmp = (1./3220)*(1.-uptmp/ustmp)
axes[ai,aj].plot(1/vtmp/1.e3,ptmp,'--',color='darkgreen',label='Extrapolated Z fit from Root et al. (2018)')
axes[ai,aj].set_ylim(0,5000)
axes[ai,aj].set_xlim(3.,10.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].legend(fontsize=sfont-5)
Out[13]:
Model Critical Point and Shock-Induced Phase Changes¶
See Davies et al. 2019 for experimentally constrained criteria for impact-vaporization of forsterite.
See Townsend et al. 2019 for ab initio calculation of the critical point of forsterite.
In [14]:
print('ANEOS Calculated Critical point:')
print(' Temperature (K): ',NewEOS.cp.T)
print(' Pressure (GPa): ', NewEOS.cp.P)
print(' Density (g/cm^3): ',NewEOS.cp.rho)
print(' Sp. Energy (MJ/kg): ', NewEOS.cp.U)
print(' Sp. Entropy (kJ/K/kg): ', NewEOS.cp.S*1.e3)
print('\n')
print('ANEOS Calculated Values at 1 bar:')
print(' Temperature at melting (K): ', NewEOS.onebar.Tmelt)
print(' Liquid density at melting (g/cm^3): ', NewEOS.onebar.rhocm)
print(' Sp. Entropy at inc. melting Sim (kJ/K/kg): ', NewEOS.onebar.Sim*1.E3)
print(' Sp. Entropy at com. melting Scm (kJ/K/kg): ', NewEOS.onebar.Scm*1.E3)
print(' Temperature at boiling (K): ', NewEOS.onebar.Tvap)
print(' Liquid density at boiling (g/cm^3): ', NewEOS.onebar.rhoiv)
print(' Sp. Entropy at inc. vaporization Siv (kJ/K/kg): ', NewEOS.onebar.Siv*1.E3)
print(' Sp. Entropy at com. vaporization Scv (kJ/K/kg): ', NewEOS.onebar.Scv*1.E3)
print('\n')
if NewEOS.tp.T > 0:
print('ANEOS Calculated Triple Point:')
print(' Temperature (K): ',NewEOS.tp.T)
print(' Pressure (GPa): ', NewEOS.tp.P)
print(' Solid density (g/cm^3): ',NewEOS.tp.rhos)
print(' Liquid density (g/cm^3): ',NewEOS.tp.rhol)
print(' Vapor density (g/cm^3): ',NewEOS.tp.rhov)
print(' Sp. Entropy at inc. melt Sim (kJ/K/kg): ', NewEOS.tp.Sim*1.E3)
print(' Sp. Entropy at com. melt Scm (kJ/K/kg): ', NewEOS.tp.Scm*1.E3)
print(' Sp. Entropy at inc. vap. Siv (kJ/K/kg): ', NewEOS.tp.Siv*1.E3)
print(' Sp. Entropy at com. vap. Scv (kJ/K/kg): ', NewEOS.tp.Scv*1.E3)
else:
print('ANEOS: No melt curve or triple point in this calculation.')
print('\n')
print('Starting at reference conditions (rho,T): ',NewEOS.R0REF,NewEOS.T0REF, ' (g/cm^3, K)')
print('ANEOS model conditions for shock-induced vaporization on release to 1 bar:')
print(' : IM CM IV 50%V CV')
print('Shock Pressure (GPa) : {:10.2f}{:10.2f}{:10.2f}{:10.2f}{:10.2f}'.format(
np.interp(NewEOS.onebar.Sim,NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.onebar.Scm,NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.onebar.Siv,NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.onebar.Siv+0.5*(NewEOS.onebar.Scv-NewEOS.onebar.Siv),NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.onebar.Scv,NewEOS.hug.S,NewEOS.hug.P)))
print('Imp. Match Vel (km/s): {:10.2f}{:10.2f}{:10.2f}{:10.2f}{:10.2f}'.format(
np.interp(NewEOS.onebar.Sim,NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.onebar.Scm,NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.onebar.Siv,NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.onebar.Siv+0.5*(NewEOS.onebar.Scv-NewEOS.onebar.Siv),NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.onebar.Scv,NewEOS.hug.S,NewEOS.hug.up)*2))
print('ANEOS model conditions for shock-induced vaporization on release to the triple point pressure:')
print(' : IM CM IV 50%V CV')
print('Shock Pressure (GPa) : {:10.2f}{:10.2f}{:10.2f}{:10.2f}{:10.2f}'.format(
np.interp(NewEOS.tp.Sim,NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.tp.Scm,NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.tp.Siv,NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.tp.Siv+0.5*(NewEOS.tp.Scv-NewEOS.tp.Siv),NewEOS.hug.S,NewEOS.hug.P),
np.interp(NewEOS.tp.Scv,NewEOS.hug.S,NewEOS.hug.P)))
print('Imp. Match Vel (km/s): {:10.2f}{:10.2f}{:10.2f}{:10.2f}{:10.2f}'.format(
np.interp(NewEOS.tp.Sim,NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.tp.Scm,NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.tp.Siv,NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.tp.Siv+0.5*(NewEOS.tp.Scv-NewEOS.tp.Siv),NewEOS.hug.S,NewEOS.hug.up)*2,
np.interp(NewEOS.tp.Scv,NewEOS.hug.S,NewEOS.hug.up)*2))
Model Phase Boundaries¶
Black lines are the ANEOS phase boundaries. Red curve is the ANEOS Hugoniot. Blue curve is the interpolated Hugoniot from the gridded eos table.
Comparison critical points from experimentally constrained quartz critical point (Kraus et al. 2012), ab initio enstatite critical point (Xiao & Stixrude 2018).
This model was developed using ab initio forsterite critical point from Townsend, J. et al. Critical point, liquid-vapor coexistence, and melting of Mg2SiO4 from ab-initio simulations. 21st Biennial Conference of the APS Topical Group on Shock Compression of Condensed Matterm Volume 64, Number 8, Abs. N2.00002. Data not shown here (in prep. for publication).
Orange diamonds are the 1-bar boiling point; orange squares are the 1-bar melting point.
Mosenfelder et al. 2007 present an estimate of the melt curve of forsterite at high pressures. For planetary applications, a forsterite EOS is often used to represent the whole mantle. For comparison, the peridotite solidus and liquidus from Fiquet et al. 2010 are shown. The estimates for the mantle solidus and liquidus span a very large range, especially when water is included; see Figure 1 in Andrault et al. 2017.
In [15]:
# PHASE DIAGRAM PLOTS
#======================LOTS OF PLOTS============================
# Plot aneos phase boundaries with focus on the vapor curve
sfont = 15
fig, axes = plt.subplots(nrows=4, ncols=2, figsize=(14,24))
plt.subplots_adjust(wspace=0.4)
#------------------------------
# entropy-temperature
ai=0
aj=0
axes[ai,aj].plot(NewEOS.vc.Sl*1.E3,NewEOS.vc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
axes[ai,aj].plot(NewEOS.vc.Sv*1.E3,NewEOS.vc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.cp.S*1.E3,NewEOS.cp.T,'o',color=stylephasept[1],markersize=stylephasept[2])
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Sl*1.E3,NewEOS.mc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.mc.Ss*1.E3,NewEOS.mc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.hug.S*1.E3,NewEOS.hug.T,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(NewEOS.hug.S[0]*1.E3,NewEOS.hug.T[0],'o',color=stylestphug[1])
axes[ai,aj].set_ylim(0,1.5*NewEOS.cp.T)
axes[ai,aj].set_xlim(0,14)
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Temperature [K]',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------------------
# density-pressure
ai=0
aj=1
axes[ai,aj].loglog(NewEOS.vc.rl,NewEOS.vc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.Pv,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.P,'o',color=stylephasept[1],markersize=stylephasept[2])
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.hug.rho,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(NewEOS.hug.rho[0],NewEOS.hug.P[0],'o',color=stylestphug[1])
axes[ai,aj].set_ylim(1.e-5,300)
axes[ai,aj].set_xlim(1.e-1,8)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#------
#entropy-pressure
ai=1
aj=0
axes[ai,aj].semilogy(NewEOS.vc.Sl*1.E3,NewEOS.vc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
axes[ai,aj].plot(NewEOS.vc.Sv*1.E3,NewEOS.vc.Pv,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.cp.S*1.E3,NewEOS.cp.P,'o',color=stylephasept[1],markersize=stylephasept[2])
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Sl*1.E3,NewEOS.mc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.mc.Ss*1.E3,NewEOS.mc.Ps,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.hug.S*1.E3,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(NewEOS.hug.S[0]*1.E3,NewEOS.hug.P[0],'o',color=stylestphug[1])
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(1.e-10,10000)
axes[ai,aj].set_xlim(0,14)
#-----------
# specific energy - pressure
ai=1
aj=1
axes[ai,aj].semilogy(NewEOS.vc.Ul,NewEOS.vc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
axes[ai,aj].plot(NewEOS.vc.Uv,NewEOS.vc.Pv,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.cp.U,NewEOS.cp.P,'o',color=stylephasept[1],markersize=stylephasept[2])
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Ul,NewEOS.mc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.mc.Us,NewEOS.mc.Ps,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.hug.U,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(NewEOS.hug.U[0],NewEOS.hug.P[0],'o',color=stylestphug[1])
axes[ai,aj].set_xlabel('Specific Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(1.e-11,10000)
axes[ai,aj].set_xlim(-3,NewEOS.cp.U*2.)
#-------
# temperature - pressure
ai=2
aj=0
axes[ai,aj].semilogy(NewEOS.vc.T,NewEOS.vc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
axes[ai,aj].plot(NewEOS.vc.T,NewEOS.vc.Pv,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.cp.T,NewEOS.cp.P,'o',color=stylephasept[1],markersize=stylephasept[2])
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.T,NewEOS.mc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.mc.T,NewEOS.mc.Ps,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.hug.T,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(NewEOS.hug.T[0],NewEOS.hug.P[0],'o',color=stylestphug[1])
axes[ai,aj].set_xlabel('Temperature (K)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_xlim(0,9000)
axes[ai,aj].set_ylim(1.e-16,100)
#-------
# pressure - temperature melt curve
ai=2
aj=1
#axes[ai,aj].plot(NewEOS.vc.Pl,NewEOS.vc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
#axes[ai,aj].plot(NewEOS.vc.Pv,NewEOS.vc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
#axes[ai,aj].plot(NewEOS.cp.P,NewEOS.cp.T,'o',color=stylephasept[1],markersize=stylephasept[2])
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Pl,NewEOS.mc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
axes[ai,aj].plot(NewEOS.mc.Ps,NewEOS.mc.T,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.hug.P,NewEOS.hug.T,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(NewEOS.hug.P[0],NewEOS.hug.T[0],'o',color=stylestphug[1])
axes[ai,aj].set_ylabel('Temperature (K)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(0,9000)
axes[ai,aj].set_xlim(-5,450)
#-------
# density - pressure melt curve
ai=3
aj=0
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2],label=styleanphase[3])
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.hug.rho,NewEOS.hug.P,stylestphug[0],linewidth=stylestphug[2],color=stylestphug[1],label=stylestphug[3])
axes[ai,aj].plot(NewEOS.hug.rho[0],NewEOS.hug.P[0],'o',color=stylestphug[1])
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(100,300)
axes[ai,aj].set_xlim(4.5,6.5)
#===================================================================
# PLOT EXPERIMENTAL CONSTRAINTS ON THE ANEOS PHASE BOUNDARIES
PLOTDATA=1
datms = 8
if PLOTDATA:
# entropy-temperature [0,0]
ai=0
aj=0
axes[ai,aj].plot(5.149,5130,'^',markersize=datms,color='cyan',label='Qtz Kraus et al. 2012')
# 0.6689 kJ/kg STP entropy from Robie et al. 1982
axes[ai,aj].plot(0.669,298,'+',color='orange',label='STP')
# 1 bar melting point entropy, enthalpy and temperature from Richet et al. 1993
#axes[ai,aj].plot(3.470,2174,'d',color='orange',label='MP 1 bar Richet et al. 1993')
# Triple point from Nagahara et al. 1994
#Triple point of forsterite 5.2e-5 bar, 1890 C (2163 K)
axes[ai,aj].plot(3.470,2163,'X',color='orange',label='TP Nagahara et al. 1994')
# density-pressure [0,1]
ai=0
aj=1
axes[ai,aj].plot([2.687,2.9468],[1.E-4,1.E-4],'<',markersize=datms,color='orange',label='MELTS MP') # Berman solid, Lange liquid
axes[ai,aj].plot(0.4822,0.1414,'+',label='En Xiao & Stixrude 2018',markersize=datms,color='brown')
axes[ai,aj].plot(0.508,0.132,'^',label='Qtz Kraus et al. 2012',markersize=datms,color='cyan')
# entropy -- pressure [1,0]
ai=1
aj=0
# 0.6689 kJ/kg STP entropy from Robie et al. 1982
axes[ai,aj].plot(0.669,1.e-4,'+',color='orange',label='STP')
# 1 bar melting point entropy, enthalpy and temperature from Richet et al. 1993
axes[ai,aj].plot(3.470,1.e-4,'d',color='orange',label='MP 1 bar Richet et al. 1993')
# Triple point from Nagahara et al. 1994
#Triple point of forsterite 5.2e-5 bar, 1890 C (2163 K)
axes[ai,aj].plot(3.470,5.2e-9,'X',color='orange',label='TP Nagahara et al. 1994')
# temperature -- pressure [2,0]
ai=2
aj=0
# Triple point from Nagahara et al. 1994
#Triple point of forsterite 5.2e-5 bar, 1890 C (2163 K)
axes[ai,aj].plot(2163.,5.2e-9,'X',color='orange',label='TP Nagahara et al. 1994')
# Melt curve points
axes[ai,aj].plot(2174,1.e-4,'d',color='orange',label='Richet et al. 1993')
axes[ai,aj].plot(2550,13.,'v',color='orange',label='de Koker et al. 2009')
# Nagahara et al. 1994 vapor curve of forsterite
tvapfo = np.arange(46)*10.+1400.+273. # in C to K
#pvapfo = np.exp(-77955.0/tvapfo+27.7)
pvapfonagahara = np.exp(169.-543.e3/(8.314*(tvapfo)))
#print(pvapfonagahara)
#print(tvapfo)
#print(pvapfo)
#axes[3,0].plot(tvapfo+273.,pvapfo*1.e5/1.e9,linestyle='-',color='orange',label='Sublimation curve\nMysen & Kushiro 1988')
#axes[3,0].plot(tvapfo,pvapfonagahara*1.e5/1.e9,linestyle='-',color='green',label='Sublimation curve\nNagahara et al. 1994')
#print(pvapfonagahara)
tt=np.zeros(7)
tt.fill(273.)
tt=tt+np.asarray([1400.,1500.,1600.,1700.,1725.,1760.,1800.])
axes[ai,aj].plot(tt,np.asarray([8.79E-9,5.98E-8,3.85E-7,2.7E-6,4.21E-6,9.58E-6,1.52E-5])/1.e4,'-x',color='orange',label='Nagahara et al. 1994')
#Centolanzi and Chapman Tektite vapor curve
tvaptek = np.arange(1400)+1700. # in K
pvaptek = np.exp(-57400.0/tvaptek+18.5)*101325. # in atm to Pa
axes[ai,aj].plot(tvaptek,pvaptek/1.e9,linestyle='-',color='cyan',label='Vapor curve tektites\nCentolanzi & Chapman 1966')
# pressure- temperature [2,1]
ai=2
aj=1
# Melt curve points
axes[ai,aj].plot(1.e-4,2174,'d',color='orange',label='Richet et al. 1993')
axes[ai,aj].plot(13.,2550,'v',color='orange',label='de Koker et al. 2009')
# Luo et al. 2004 reanalyzed temperature point
#5.86(15) 4810(70) 188(6)
axes[ai,aj].errorbar([188],[4810],xerr=[6],yerr=[70],fmt='^',color='orange',label='Luo et al. 2004 Olivine')
axes[ai,aj].plot(Mosenfelderdatarr.iloc[:,0].values,Mosenfelderdatarr.iloc[:,1].values,linestyle='-',color='brown',linewidth=1,label='Forsterite Melt Curve\n(Mosenfelder et al. 2007)')
axes[ai,aj].plot(peridotiteliquidusdatarr.iloc[:,0].values,peridotiteliquidusdatarr.iloc[:,1].values,linestyle='-',color='orange',label='Peridotite Liquidus')
axes[ai,aj].plot(peridotitesolidusdatarr.iloc[:,0].values,peridotitesolidusdatarr.iloc[:,1].values,linestyle=':',color='orange',label='Peridotite Solidus\n(Fiquet et al. 2010)')
#####OMEGA data from Root et al. 2018
col=local_cmaps.parula(0.5)
axes[ai,aj].fill_between(OM_D1P*1000,(OM_DT1-OM_DTe1),(OM_DT1+OM_DTe1),label="OMEGA data (Root et al. 2018)",
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D2P*1000,(OM_DT2-OM_DTe2),(OM_DT2+OM_DTe2),
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D3P*1000,(OM_DT3-OM_DTe3),(OM_DT3+OM_DTe3),
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D4P*1000,(OM_DT4-OM_DTe4),(OM_DT4+OM_DTe4),
color=col,alpha=0.25)
axes[ai,aj].plot(QMDH_p[1::],QMDH_t[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].errorbar(ZTdat_p,ZTdat_t,xerr=ZTdat_perr,yerr=ZTdat_terr/1.E3,fmt=stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3],elinewidth=1)
# density - pressure [3,0]
ai=3
aj=0
# Melt Hugoniot Points from Mosenfelder et al. 2007
axes[ai,aj].errorbar([5.48],[188.5],xerr=[0.6],yerr=[2.0],fmt='o',color='orange',label='Hugoniot "melt point" from\nMosenfelder et al. 2007')
# QMD Root et al. 2018
axes[ai,aj].plot(QMDH_r[1::],QMDH_p[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].errorbar(Zdat_r,Zdat_p,xerr=Zdat_rerr,yerr=Zdat_perr,fmt=stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3])
# Luo et al. 2004 reanalyzed temperature point
#5.86(15) 4810(70) 188(6)
axes[ai,aj].errorbar([5.86],[188],xerr=[0.15],yerr=[6],fmt='^',color='orange',label='Luo et al. 2004 Olivine')
# don't show a plot in lower right
axes[3,1].axis("off")
axes[0,0].legend(fontsize=sfont-5)
axes[0,1].legend(fontsize=sfont-5)
axes[1,0].legend(fontsize=sfont-5)
axes[1,1].legend(fontsize=sfont-5)
axes[2,0].legend(fontsize=sfont-5)
axes[2,1].legend(fontsize=sfont-5)
axes[3,0].legend(fontsize=sfont-5)
plt.tight_layout(pad=0.6)
#plt.savefig('phase-diagram-fig.pdf', format='pdf', dpi=1000,transparent=True)
#--------
ANEOS model comparisons to experimental data¶
The 1-bar boiling point of forsterite has not been measured. In the liquid field, we assume that the heat capacity is constant at the value reported in Thomas and Asimow 2013.
The volume change on melting forsterite is very large ($\rho_l/\rho_s=0.905$). The slope of the melt curve is incorrect at high pressures when this value is used. So the modeled density change is smaller than the true value at low pressures. As a result, the model density of liquid forsterite at the triple point is too large.
In [16]:
# INCLUDE A COMPARISON TO EARTH'S STRUCTURE PREM MODEL
G = 6.67E-11 # Gravitational constant m3/kg/s2
# Read in PREM: Preliminary Earth Reference Model
PREM_filename=datadir+'PREM500_IDV.csv' # we love long, readable variable names!
# make a class to hold the PREM data
class PREMclass:
"""Class to hold PREM data and other 1-D Earth variables.""" # this is a documentation string for this class
def __init__(self): # self is the default name of the object for internal referencing of the variables in the class
"""A function to initialize the class object.""" # this is a documentation string for this function
self.NR = 0 # number of radius points
self.radius = np.zeros(self.NR)
self.density = np.zeros(self.NR)
self.pwavevel = np.zeros(self.NR)
self.swavevel = np.zeros(self.NR)
self.pressure = np.zeros(self.NR)
self.temperature = np.zeros(self.NR)
# not going to use all the variables in the file
self.units = '' # I like to keep a text note in a structure about the units
# initialize an empty PREM object
PREM = PREMclass()
# read the data into the class parameters
PREM.radius = np.loadtxt(PREM_filename,delimiter=',',skiprows=2,usecols=[0]) # radius in m
PREM.density = np.loadtxt(PREM_filename,delimiter=',',skiprows=2,usecols=[1]) # density in kg/m3
PREM.pwavevel = np.loadtxt(PREM_filename,delimiter=',',skiprows=2,usecols=[2]) # p-wave velocity m/s
PREM.swavevel = np.loadtxt(PREM_filename,delimiter=',',skiprows=2,usecols=[3]) # s-wave velocity m/s
PREM.NR = len(PREM.radius) # number of radius points
PREM.units = 'radius (m), density (kg/m3), pwavevel (m/s), swavevel (m/s)'
# start at the surface and integrate via a for loop to the center of the planet
# calculate the thickness of each layer in the PREM model using the roll function
PREM_dr = np.roll(PREM.radius,-1)-PREM.radius
PREM_dr[PREM.NR-1] = 0. # we are not using the last entry in the list because there are NR-1 layers
#print(PREM_dr)
# calculate the mass of each layer
# density x area x thickness of each layer
PREM_mass_rad = PREM.density*(4.*np.pi*PREM.radius*PREM.radius*PREM_dr)
# Check that the total mass is the mass of the Earth
#print('PREM total mass (kg)=',np.sum(PREM_mass_rad))
#print('PREM total mass (Mearth)=',np.sum(PREM_mass_rad)/5.972E24)
PREM.pressure = np.zeros(PREM.NR) # make array of zeros for pressure of the same length as the arrays in the PREM model
# The first entry is the middle of the planet, so start at the surface and integrate inwards
for i in range(PREM.NR-2,0,-1):
# we indent for the code in the for loop
PREM.pressure[i] = PREM.pressure[i+1]+G*np.sum(PREM_mass_rad[0:i-1])*PREM.density[i]*PREM_dr[i]/PREM.radius[i]/PREM.radius[i]
# use SESAME units
PREM.pressure = PREM.pressure/1.E9 # GPa
# first extract the isentropes for the planet from the EOS tables
mantle = isentrope_class() # code in eostable.py
ForsteriteEOS = NewEOS
Smantle = 0.0027 # MJ/K/kg
# loop across all densities and extract the values for the requested isentrope
for i in range(0,ForsteriteEOS.ND):
ind = np.where((ForsteriteEOS.S[:,i] > 0))[0]
interpfunction = interpolate.interp1d(ForsteriteEOS.S[ind,i],ForsteriteEOS.P[ind,i]) # MJ/K/kg, GPa
mantle.pressure = np.append(mantle.pressure,interpfunction(Smantle)) # GPa
interpfunction = interpolate.interp1d(ForsteriteEOS.S[ind,i],ForsteriteEOS.T[ind]) # MJ/K/kg, GPa
mantle.temperature = np.append(mantle.temperature,interpfunction(Smantle)) # GPa
mantle.density = ForsteriteEOS.rho # g/cm3
print('Calculated forsterite isentrope with ',np.round(np.interp(1.E-4,mantle.pressure,mantle.temperature)),' K potential temperature')
In [17]:
# 1-bar plots and 298 K plots
# Plot aneos vapor curves
sfont = 15
fig, axes = plt.subplots(2, 2, figsize=(14,14))
plt.subplots_adjust(wspace=0.4)
#--------
# temperature - entropy at 1 bar
ai=0
aj=0
axes[ai,aj].plot(Gilletdatarr.iloc[:,0].values,Gilletdatarr.iloc[:,1].values/1.e3,linestyle='-',color='brown',linewidth=6,label='Gillet et al. 1991')
axes[ai,aj].plot(Gilletdatarr.iloc[:,2].values,Gilletdatarr.iloc[:,3].values/1.e3,linestyle='-',color='orange',linewidth=6,label='Thomas & Asimow 2013')
axes[ai,aj].plot(NewEOS.onebar.T,NewEOS.onebar.S*1.E3,'+',color='blue',label='ANEOS 1 bar')
axes[ai,aj].set_xlabel('Temperature (K)',size=sfont)
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_title('1-bar isobar',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(0,10)
axes[ai,aj].set_xlim(0,4000)
#----
# density-temperature at 1 bar
ai=0
aj=1
axes[ai,aj].plot(NewEOS.onebar.T,NewEOS.onebar.rho,'+',color='blue',label='ANEOS 1 bar')
axes[ai,aj].set_ylabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_xlabel('Temperature (K)',size=sfont)
axes[ai,aj].set_title('1-bar isobar',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(1,4)
axes[ai,aj].set_xlim(0,4000)
# plot data
axes[ai,aj].plot(1890+273.,2.968,'s',color='orange',label='MELTS MP Berman')
axes[ai,aj].plot(1890+273.,2.687,'o',color='orange',label='MELTS MP Lange')
axes[ai,aj].plot(2273.,2.597,'d',color='orange',label='Thomas & Asimow 2013')
#----
# density-pressure at 298 K
ai=1
aj=0
iT0REF = np.where(NewEOS.T == T0REF)[0]
axes[ai,aj].plot(NewEOS.rho,NewEOS.P[iT0REF[0],:],'-',color='blue',label='ANEOS 298-K isotherm')
# Finkelstein et al. 2014 Forsterite isotherm
K0T = 130.0 # +-9 GPa
K0Tp = 4.12 # +- 0.07
BM_pressure = 1.5*K0T*(np.power(NewEOS.rho/NewEOS.R0REF,7./3.)-np.power(NewEOS.rho/NewEOS.R0REF,5./3.)
)*(1.+0.75*(K0Tp-4.)*(np.power(NewEOS.rho/NewEOS.R0REF,2./3.)-1.))
K0T = 130.0-9. # +-9 GPa
K0Tp = 4.12 # +- 0.07
BM_pressure_low = 1.5*K0T*(np.power(NewEOS.rho/NewEOS.R0REF,7./3.)-np.power(NewEOS.rho/NewEOS.R0REF,5./3.)
)*(1.+0.75*(K0Tp-4.)*(np.power(NewEOS.rho/NewEOS.R0REF,2./3.)-1.))
K0T = 130.0+9. # +-9 GPa
K0Tp = 4.12 # +- 0.07
BM_pressure_high = 1.5*K0T*(np.power(NewEOS.rho/NewEOS.R0REF,7./3.)-np.power(NewEOS.rho/NewEOS.R0REF,5./3.)
)*(1.+0.75*(K0Tp-4.)*(np.power(NewEOS.rho/NewEOS.R0REF,2./3.)-1.))
igood = np.where(BM_pressure < 48.)
axes[ai,aj].plot(NewEOS.rho[igood],BM_pressure[igood],'-',color='green',label='Fo 298-K isotherm\nFinkelstein et al. 2014')
igood = np.where(BM_pressure_low < 48.)
axes[ai,aj].plot(NewEOS.rho[igood],BM_pressure_low[igood],'--',color='green')
igood = np.where(BM_pressure_high < 48.)
axes[ai,aj].plot(NewEOS.rho[igood],BM_pressure_high[igood],'--',color='green')
# Jacobsen et al. 2008 MgO isotherm
K0T = 159.6 # +-0.6 GPa room temp isotherm
K0Tp = 3.74 # +-0.03
R00 = (24.305+15.999)*4.*1.6726/(74.697*1.E-3)/1.E3 # kg/m3->g/cm3
print(R00)
BM_pressure = 1.5*K0T*(np.power(NewEOS.rho/R00,7./3.)-np.power(NewEOS.rho/R00,5./3.)
)*(1.+0.75*(K0Tp-4.)*(np.power(NewEOS.rho/R00,2./3.)-1.))
igood = np.where((BM_pressure > 25.)&(BM_pressure < 125.))
axes[ai,aj].plot(NewEOS.rho[igood],BM_pressure[igood],'-',color='brown',label='MgO 298-K isotherm\nJacobsen et al. 2008')
# Vanpeteghem et al. 2006 silicate perovskite isotherm
K0T = 253. # +-1 GPa room temp isotherm
K0Tp = 4.0
R00 = (24.305+28.085+3.*15.999)*4.*1.6726/(162.51*1.E-3)/1.E3 # kg/m3->g/cm3
print(R00)
BM_pressure = 1.5*K0T*(np.power(NewEOS.rho/R00,7./3.)-np.power(NewEOS.rho/R00,5./3.)
)*(1.+0.75*(K0Tp-4.)*(np.power(NewEOS.rho/R00,2./3.)-1.))
igood = np.where((BM_pressure > 25.)&(BM_pressure < 125.))
axes[ai,aj].plot(NewEOS.rho[igood],BM_pressure[igood],'-',color='orange',label='MgSiO$_3$ Pv 298-K isotherm\nVanpeteghem et al. 2006')
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_title('298-K isotherm',size=sfont)
axes[ai,aj].set_xlim(3,6)
axes[ai,aj].set_ylim(0,140)
#----
# density-pressure at 298 K
ai=1
aj=1
axes[ai,aj].plot(mantle.density,mantle.pressure,'-',color='blue',label='ANEOS '+str(np.round(np.interp(1.E-4,mantle.pressure,mantle.temperature)))+' K isentrope',markersize=10)
axes[ai,aj].plot(PREM.density/1.E3,PREM.pressure,'-',color='orange',label='PREM')
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_title('PREM and '+str(np.round(np.interp(1.E-4,mantle.pressure,mantle.temperature)))+' K ANEOS model isentrope',size=sfont)
axes[ai,aj].set_xlim(2,6)
axes[ai,aj].set_ylim(0,140)
# don't show a plot in lower right
#axes[1,1].axis("off")
axes[0,0].legend(fontsize=sfont-5)
axes[0,1].legend(fontsize=sfont-5)
axes[1,0].legend(fontsize=sfont-5)
axes[1,1].legend(fontsize=sfont-5)
Out[17]:
ANEOS Gruneisen parameter and Theta parameter for thermal model¶
The Gruneisen parameter in forsterite liquid has been determined experimentally from shock wave data (Thomas & Asimow 2013; Davies et al. in prep.). Shockwave data derive the Grueneisen parameter in reference to a known state: \begin{equation} \gamma = \frac{1}{\rho}\frac{(P-P_{\rm ref})}{(E-E_{\rm ref})} \bigg\rvert _V \end{equation}
The ANEOS Gruneisen model is split into two parts. For $\rho \ge \rho_{0}$, \begin{equation} \gamma = \left( \frac{\gamma_0 \rho_0}{\rho} + C_{24} \left( 1-\frac{\rho_0}{\rho} \right)^2 \right) (1-C_{60}) + \left( \gamma_0 + (C_{24}-\gamma_0) \left( 1- \frac{\rho_0}{\rho} \right)^2 \right) C_{60}. \end{equation} For $\rho < \rho_{0}$, \begin{equation} \gamma = C_{16} \rho^2 + C_{17}\rho + 1 + C_{61}. \end{equation}
$C_{16}$ and $C_{17}$ are calculated so that $\gamma$ and $d \gamma / d \rho$ are continuous at $\rho=\rho_0$. The model asymptotes to the Thomas-Fermi limit ($\gamma=2/3$) when $C_{24}=2/3$.
The functional form in ANEOS does not provide a good fit to the data on forsterite. As a result, the model Gruneisen parameter does not extrapolate to the Thomas-Fermi limit at high pressures.
In [18]:
# plot the gamma and isotherms
# ANEOS Formulation for Gamma and theta
theta0=abs(NewEOS.theta0)
rhoarr = (1+np.arange(1000))/1000.*NewEOS.R0REF*10.
gammaarr = (NewEOS.gamma0*NewEOS.R0REF/rhoarr
)+NewEOS.C24*np.power(1.0-NewEOS.R0REF/rhoarr,2.)*(1.-NewEOS.C60)+(NewEOS.gamma0 + (NewEOS.C24-NewEOS.gamma0)*np.power(1.-NewEOS.R0REF/rhoarr,2.))*NewEOS.C60
s3 = NewEOS.C61+1.
C14 = theta0 * np.exp(1.5*s3-(2.-0.5*NewEOS.C60)*NewEOS.gamma0)/(np.power(NewEOS.R0REF,s3))
C16 = (s3-(2.-NewEOS.C60)*NewEOS.gamma0)/(NewEOS.R0REF*NewEOS.R0REF)
C17 = ((3.-NewEOS.C60)*NewEOS.gamma0-2.*s3)/NewEOS.R0REF
gammaarrlow = C16*rhoarr*rhoarr+C17*rhoarr+s3
thetaarr = theta0*np.exp((1.-NewEOS.C60)*(1.-NewEOS.R0REF/rhoarr)*NewEOS.gamma0-0.5*(NewEOS.R0REF/rhoarr)*(3.-(NewEOS.R0REF/rhoarr)*(4-(NewEOS.R0REF/rhoarr))))*np.power((rhoarr/NewEOS.R0REF),NewEOS.C24)
thetalowarr = C14*np.exp(rhoarr*(C17+0.5*C16*rhoarr))*np.power(rhoarr,s3)
#-------- plots
sfont = 15
fig, axes = plt.subplots(1, 2, figsize=(14,8))
plt.subplots_adjust(wspace=0.4)
# -----
ai=0
indlow = np.where(rhoarr <= NewEOS.R0REF)
indhigh = np.where(rhoarr >= NewEOS.R0REF)
axes[ai].plot(rhoarr[indhigh[0]],gammaarr[indhigh[0]],label="ANEOS Gamma-high",color='black')
axes[ai].plot(rhoarr[indlow[0]], gammaarrlow[indlow[0]],label="ANEOS Gamma-low",color='black',ls='--')
axes[ai].plot(NewEOS.R0REF,NewEOS.gamma0,'+',label="ANEOS Gamma0",color='black')
axes[ai].set_ylim(0,2.5)
axes[ai].set_xlim(0,8)
axes[ai].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai].set_ylabel('Gamma (-)',size=sfont)
axes[ai].tick_params(labelsize=sfont)
# solid forsterite at STP
axes[ai].plot([3.22],[1.29],'s',color='red',label='Fo solid STP')
# Thomas and Asimow 2013 liquid forsterite shock data
gamma_0=0.396
q=-2.02
q_u=1.03
Rho_0=2597. # kg/m^3
asi_rhot = np.array([3739.79122056, 3335.90237636,4691.02371542 ,4088.40354767, 4347.15217391 ,4681.1865942 ])
##asi_rhot=np.array([3340.0, 3740.0, 4100.0, 4680.0, 5290.0, 5420.0]) # BAD TABULATED VALUES in TA13
asi_gammat=gamma_0*np.power(Rho_0/asi_rhot,q)
asi_rho = np.append([2597.],asi_rhot)/1.e3
asi_gamma = np.append([0.396],asi_gammat)
#print(asi_rho)
#print(asi_gamma)
#[3739.79122056 3335.90237636 4691.02371542 4088.40354767 4347.15217391 4681.1865942 ]
#[0.82720568 0.65667847 1.30744208 0.99037675 1.12107749 1.30190973]
# Erik's error bars monte carlo'd for the asimow data
#gamma [ 0.82271901 0.65485213 1.29584059 0.97276836 1.11171104 1.29195917]
asi_gamma_sig_low=np.asarray([0., 0.25715384 , 0.14948592 , 0.5898531, 0.36154228 , 0.45607297 , 0.58790934])
asi_gamma_sig_high=np.asarray([0., 0.37855329, 0.19525818 , 1.09577441, 0.6137275 , 0.78965792 , 1.08676142])
axes[ai].plot(asi_rho,asi_gamma,'o',color='orange',label='Forsterite liq.\nTA13 corrected')
for i in range(0,len(asi_gamma)):
axes[ai].plot([asi_rho[i],asi_rho[i]],[asi_gamma[i]-asi_gamma_sig_low[i],asi_gamma[i]+asi_gamma_sig_high[i]],linestyle='-',color='orange')
# these values from the submitted paper
axes[ai].errorbar(SR_rho,SR_gamma,yerr=SR_gamma_e, xerr=SR_rho_e, fmt='g+', label ='Forsterite liq. Z data\nDavies et al. 2019')
# -----
ai=1
axes[ai].plot(rhoarr[indhigh[0]],thetaarr[indhigh[0]],label="ANEOS Theta-high",color='black')
axes[ai].plot(rhoarr[indlow[0]],thetalowarr[indlow[0]],label="ANEOS Theta-low",color='black',ls='--')
axes[ai].plot(NewEOS.R0REF,theta0,'+',label="Theta0",color='black')
axes[ai].set_ylim(0,10000)
axes[ai].set_xlim(0,8)
axes[ai].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai].set_ylabel('Theta (K)',size=sfont)
axes[ai].tick_params(labelsize=sfont)
axes[0].legend(fontsize=sfont-5)
axes[1].legend(fontsize=sfont-5)
Out[18]:
Specfic Heat Capacity and Sounds Speeds¶
The calculated heat capacities on the forsterite Hugoniot in the liquid region, from Root et al. 2018, are similar to the 1-bar value derived from Thomas and Asimow 2013. Both are larger than the 3nR high temperature value for the solid (Gillet et al. 1991).
In [19]:
sfont = 15
fig, axes = plt.subplots(2, 2, figsize=(14,14))
plt.subplots_adjust(wspace=0.4)
#-----------------------------
# Pick isotherms and set color scale
ixtemparr = [298.,1000.,2050.,2300.,5000.,8000.,20000.]
# set color scale same for all plots
tcolmin=0.
tcolmax=20000.
# find the index closest to the selected temperatures -- no interpolation
ixindarr=np.zeros(len(ixtemparr))
ixlabelarr = []
for i in np.arange(len(ixtemparr)):
tmpi=int(np.round(np.interp(ixtemparr[i],NewEOS.T,np.arange(NewEOS.NT))))
#print(tmpi,antarr[tmpi])
ixindarr[i] = tmpi
ixlabelarr.append(str(ixtemparr[i])+' K')
#-----------------------
ai=0
aj=0
for i in np.arange(len(ixtemparr)):
icolscale = (ixtemparr[i]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.cv[int(ixindarr[i]),:]*1000.,c=col,linestyle='-',label=ixlabelarr[i])
axes[ai,aj].plot(QMDH_r1,QMDH_cv*1000.,styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label='QMD Hugoniot\n(Root et al. 2018')
axes[ai,aj].plot(2.597,1.73736,'^',color='orange',label='1 bar 2273 K liquid Cv\n(Thomas & Asimow 20133)')
axes[ai,aj].plot(3.,180./(NewEOS.FMW/1.E3)/1.E3,'s',color='orange',label='1 bar 2000 K solid Cv\n(Gillet et al. 1991)')
axes[ai,aj].set_ylim(1.,5.)
axes[ai,aj].set_xlim(0,10)
axes[ai,aj].set_ylabel('Specific heat capacity Cv (kJ/K/kg)',size=sfont)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-----------------------
ai=0
aj=1
for i in np.arange(len(ixtemparr)):
icolscale = (ixtemparr[i]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.cv[int(ixindarr[i]),:]*1000.*1000./7/8.314*0.14,c=col,linestyle='-',label=ixlabelarr[i])
axes[ai,aj].plot(QMDH_r1,QMDH_cv*1.E6/7/8.314*0.14,styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label='QMD Hugoniot\n(Root et al. 2018')
axes[ai,aj].plot(2.597,1737./7/8.314*0.140,'^',color='orange',label='1 bar 2273 K liquid Cv\n(Thomas & Asimow 2013)')
axes[ai,aj].plot(3.,180./(NewEOS.FMW/1.E3)/7/8.314*0.140,'s',color='orange',label='1 bar 2000 K solid Cv\n(Gillet et al. 1991)')
axes[ai,aj].set_ylim(1.,10.)
axes[ai,aj].set_xlim(0,10)
axes[ai,aj].set_ylabel('Specific heat capacity Cv (nR)',size=sfont)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-----------------------
# plot sound speed along isotherms
ai=1
aj=0
for i in np.arange(len(ixtemparr)):
icolscale = (ixtemparr[i]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.P[int(ixindarr[i]),:],NewEOS.cs[int(ixindarr[i]),:]/1.e5,c=col,linestyle='-',label=ixlabelarr[i])
axes[ai,aj].plot(1.e-4,2.674,'d',color='orange',label='Thomas & Asimow 2013 2273 K')
axes[ai,aj].set_ylim(0,10)
axes[ai,aj].set_xlim(-10,40)
axes[ai,aj].set_ylabel('Bulk Sound Speed (km/s)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-----------------------
# plot sound speed along isotherms
ai=1
aj=1
for i in np.arange(len(ixtemparr)):
icolscale = (ixtemparr[i]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.P[int(ixindarr[i]),:],NewEOS.cs[int(ixindarr[i]),:]/1.e5,c=col,linestyle='-',label=ixlabelarr[i])
axes[ai,aj].plot(1.e-4,2.674,'d',color='orange',label='Thomas & Asimow 2013 2273 K')
axes[ai,aj].set_ylim(0,20)
axes[ai,aj].set_xlim(0,700)
axes[ai,aj].set_ylabel('Bulk Sound Speed (km/s)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[0,0].legend(fontsize=sfont-5)
axes[0,1].legend(fontsize=sfont-5)
axes[1,0].legend(fontsize=sfont-5)
axes[1,1].legend(fontsize=sfont-5)
Out[19]:
FIGURES FOR STEWART ET AL. SCCM19, REVISED¶
Stewart, S., et al. (in revision). The shock physics of giant impacts: Key requirements for the equations of state. In J. Lane, T. Germann, and M. Armstrong (Eds.), 21st Biennial APS Conference on Shock Compression of Condensed Matter (SCCM19). AIP Publishing.
Tillotson parameters for olivine¶
Tillotson is a simple pressure-volume-internal energy equation of state model that was developed for metals (Tillotson 1962). Temperature is typically approximated by a constant heat capacity. Here, I have not implemented a temperature calculation.
There are no true phase boundaries but there is a split in the EOS between condensed and gas regions with an interpolated region.
Here are the material parameters selected for olivine by Marinova et al. Icarus 2011 (used by Hosono et al. 2019):
$\rho_0$ = Reference density at zero pressure = 3500 kg/m$^3$
$A$ = Bulk modulus $K_0$ = 131e9 Pa
$B$ = B constant = 49e9 Pa
$E_0$ = E0 contant (NOT reference state specific internal energy) = 550e6 J/kg
$a$ = a constant = 0.5 [-]
$b$ = b constant = 1.4 [-]
$\alpha$ = $\alpha$ constant = 5 [-]
$\beta$ = $\beta$ constant = 5 [-]
$E_{IV}$ = specific internal energy of incipient vaporization = 4.5e6 J/kg
$E_{CV}$ = specific internal energy of complete vaporization = 14.5e6 J/kg
The sum of constants $a$ and $b$ is the Mie-Gruneisen parameter at the reference density: $a+b = \Gamma(\rho_0)$
Here, I have coded two different implementations of Tillotson: (1) from Hosono et al. Nature Geoscience 2019 and (2) from iSALE Dellen version. There are some slight differences but the overall topology of the EOS are the same.
Because the Tillotson equations produce large negative pressure values when $\rho<\rho_0$ and $E<E_{CV}$, the EOS is implemented with a pressure minimum that varies between implementations and papers. Here, I set the pressure in the cold region to the minimum value before interpolating. In the original codes for iSALE and Hosono et al. 2019, the interpolated region was calculated prior to resetting to a pressure minimum. To see the difference, switch between the Hosono and iSALE functions at the bottom of the next code cell.
The Tillotson functions are in the next code cell.
In [20]:
# Calculate a Tillotson EOS grid
# the grid is used to make some differential calculations below
# Tillotson EOS functions are in the file eostable.py
# dunite tillotson parameters used by Hosono et al. 2019
# are taken from the olivine parameters in Marinova et al. 2011 Icarus
# parameters: [rho0, E0, EIV, ECV, AA, BB, a, b, alpha, beta]
# units: [kg/m3, J/kg, J/kg, J/kg, Pa, Pa, [-]x4]
olivinetill = [3500.0, 550.0e+6, 4.500e+6, 14.50e+6, 131.00e+9, 49.00e+9, 0.5, 1.4, 5.0, 5.0]
# Basalt parameters from iSALE -- from where? Benz?
#basalttill = [2650.0, 4.87E8, 4.72E6, 18.2E6, 5.3E10, 5.3E10, 0.6, 0.6, 5., 5.]
#-------------------------
# Make a class to hold the Tillotson EOS using Hosono functions
TillEOS = TillotsonClass() # initialize empty structure
TillEOS.ND = NewEOS.ND
TillEOS.NU = len(tillearr)
TillEOS.rho = NewEOS.rho # g/cm3 Use same density array as ANEOS SESAME table
TillEOS.U = tillearr # MJ/kg Grid set up in the grid code cell near top of this notebook
TillEOS.FillTable(matparams=olivinetill,modelname='Olivine Marinova et al. 2011') # This function uses Hosono's EOS implementation
TillEOS.calchugoniot(r00=olivinetill[0]/1.E3,e0=0) # calculate the principal Hugoniot
In [21]:
# Load older ANEOS models for comparison
# Load in Canup 2013 model
# READ IN NEW ANEOS MODEL and fill the extEOStable class object
# source in eostable.py
#------------------------------------------------------------------
subdir = 'aneos-canup/'
MODELNAME = 'Canup2013 Forsterite'
# Header information must all be compatible with float format
MATID = 1.0 # MATID number
DATE = 190802. # Date as a single 6-digit number YYMMDD
VERSION = 1.0 # ANEOS Parameters Version number
FMN = 70. # Formula weight in atomic numbers for Mg2SiO4
FMW = 140.691 # Formula molecular weight (g/cm3) for Mg2SiO4
# The following define the default initial state for material in the 201 table
R0REF = 3.32 # g/cm3 *** R0REF is inserted into the density array
K0REF = 1.446E12 # dynes/cm2 K0=rho0*cs0^2
T0REF = 298. # K -- *** T0REF is inserted into the temperature array
P0REF = 1.E6 # dynes/cm2 -- this defines the principal Hugoniot calculated below
CanupEOS = extEOStable() # FIRST make new empty EOS object
CanupEOS.loadextsesame(subdir+'NEW-SESAME-EXT.TXT') # LOAD THE EXTENDED 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
CanupEOS.loadstdsesame(subdir+'NEW-SESAME-STD.TXT') # LOAD THE STANDARD 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
CanupEOS.MODELNAME = MODELNAME # string set above in user input
CanupEOS.MDQ = np.zeros((CanupEOS.NT,CanupEOS.ND)) # makes the empty MDQ array
#print(CanupEOS.units) # these are the default units for SESAME rho-T tables
#'Units: g/cm3, K, GPa, MJ/kg, MJ/kg, MJ/K/kg, cm/s, MJ/K/kg, KPA flag. 2D arrays are (NT,ND).'
# Add the header info to the table. This could be done during the loading.
# if made from this notebook, these values are set in the user-input above.
# ** MAKE SURE THEY MATCH ANEOS.INPUT **
CanupEOS.MATID = MATID
CanupEOS.DATE = DATE
CanupEOS.VERSION = VERSION
CanupEOS.FMN = FMN
CanupEOS.FMW = FMW
CanupEOS.R0REF = R0REF
CanupEOS.K0REF = K0REF
CanupEOS.T0REF = T0REF
CanupEOS.P0REF = P0REF
#
# Load the information from ANEOS.INPUT and ANEOS.OUTPUT
CanupEOS.loadaneos(aneosinfname=subdir+'ANEOS.INPUT',aneosoutfname=subdir+'ANEOS.OUTPUT',silent=True)
#
# calculate the principal Hugoniot from the table
CanupEOS.calchugoniot(r0=CanupEOS.R0REF,t0=CanupEOS.T0REF)
#
# calculate the 1-bar profile; loop over temp
CanupEOS.onebar.T = np.zeros(CanupEOS.NT)
CanupEOS.onebar.S = np.zeros(CanupEOS.NT)
CanupEOS.onebar.rho = np.zeros(CanupEOS.NT)
it0 = np.where(CanupEOS.T >= CanupEOS.T0REF)[0]
id0 = np.arange(CanupEOS.ND)#np.where(CanupEOS.rho >= 0.8*CanupEOS.R0REF)[0]
for iit in range(0,CanupEOS.NT):
CanupEOS.onebar.T[iit] = CanupEOS.T[iit]
CanupEOS.onebar.S[iit] = np.interp(1.E-4,CanupEOS.P[iit,id0],CanupEOS.S[iit,id0])
CanupEOS.onebar.rho[iit] = np.interp(1.E-4,CanupEOS.P[iit,id0],CanupEOS.rho[id0])
#print(iit,CanupEOS.onebar.rho[iit],CanupEOS.onebar.T[iit],CanupEOS.onebar.S[iit]*1.E3)
In [22]:
# Load older ANEOS models for comparison
# Load in GADGET model (Robert Marcus Thesis; Cuk & Stewart 2012)
# READ IN NEW ANEOS MODEL and fill the extEOStable class object
# source in eostable.py
#------------------------------------------------------------------
subdir = 'aneos-gadget/'
MODELNAME = 'GADGET2 Forsterite'
# Header information must all be compatible with float format
MATID = 1.0 # MATID number
DATE = 190802. # Date as a single 6-digit number YYMMDD
VERSION = 1.0 # ANEOS Parameters Version number
FMN = 70. # Formula weight in atomic numbers for Mg2SiO4
FMW = 140.691 # Formula molecular weight (g/cm3) for Mg2SiO4
# The following define the default initial state for material in the 201 table
R0REF = 3.32 # g/cm3 *** R0REF is inserted into the density array
K0REF = 1.446E12 # dynes/cm2 K0=rho0*cs0^2
T0REF = 298. # K -- *** T0REF is inserted into the temperature array
P0REF = 1.E6 # dynes/cm2 -- this defines the principal Hugoniot calculated below
GadgetEOS = extEOStable() # FIRST make new empty EOS object
GadgetEOS.loadextsesame(subdir+'NEW-SESAME-EXT.TXT') # LOAD THE EXTENDED 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
GadgetEOS.loadstdsesame(subdir+'NEW-SESAME-STD.TXT') # LOAD THE STANDARD 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
GadgetEOS.MODELNAME = MODELNAME # string set above in user input
GadgetEOS.MDQ = np.zeros((GadgetEOS.NT,GadgetEOS.ND)) # makes the empty MDQ array
#print(GadgetEOS.units) # these are the default units for SESAME rho-T tables
#'Units: g/cm3, K, GPa, MJ/kg, MJ/kg, MJ/K/kg, cm/s, MJ/K/kg, KPA flag. 2D arrays are (NT,ND).'
# Add the header info to the table. This could be done during the loading.
# if made from this notebook, these values are set in the user-input above.
# ** MAKE SURE THEY MATCH ANEOS.INPUT **
GadgetEOS.MATID = MATID
GadgetEOS.DATE = DATE
GadgetEOS.VERSION = VERSION
GadgetEOS.FMN = FMN
GadgetEOS.FMW = FMW
GadgetEOS.R0REF = R0REF
GadgetEOS.K0REF = K0REF
GadgetEOS.T0REF = T0REF
GadgetEOS.P0REF = P0REF
#
# Load the information from ANEOS.INPUT and ANEOS.OUTPUT
GadgetEOS.loadaneos(aneosinfname=subdir+'ANEOS.INPUT',aneosoutfname=subdir+'ANEOS.OUTPUT',silent=True)
#
# calculate the principal Hugoniot from the table
GadgetEOS.calchugoniot(r0=GadgetEOS.R0REF,t0=GadgetEOS.T0REF)
#
# calculate the 1-bar profile; loop over temp
GadgetEOS.onebar.T = np.zeros(GadgetEOS.NT)
GadgetEOS.onebar.S = np.zeros(GadgetEOS.NT)
GadgetEOS.onebar.rho = np.zeros(GadgetEOS.NT)
it0 = np.where(GadgetEOS.T >= GadgetEOS.T0REF)[0]
id0 = np.arange(GadgetEOS.ND)#np.where(GadgetEOS.rho >= 0.8*GadgetEOS.R0REF)[0]
for iit in range(0,GadgetEOS.NT):
GadgetEOS.onebar.T[iit] = GadgetEOS.T[iit]
GadgetEOS.onebar.S[iit] = np.interp(1.E-4,GadgetEOS.P[iit,id0],GadgetEOS.S[iit,id0])
GadgetEOS.onebar.rho[iit] = np.interp(1.E-4,GadgetEOS.P[iit,id0],GadgetEOS.rho[id0])
#print(iit,GadgetEOS.onebar.rho[iit],GadgetEOS.onebar.T[iit],GadgetEOS.onebar.S[iit]*1.E3)
In [23]:
# Load older ANEOS models for comparison
# Load in ISALE-Dellen model; Collins & Melosh LPSC 2014
# READ IN NEW ANEOS MODEL and fill the extEOStable class object
# source in eostable.py
#------------------------------------------------------------------
subdir = 'aneos-isale/'
MODELNAME = 'ISALE Forsterite'
# Header information must all be compatible with float format
MATID = 1.0 # MATID number
DATE = 190802. # Date as a single 6-digit number YYMMDD
VERSION = 1.0 # ANEOS Parameters Version number
FMN = 70. # Formula weight in atomic numbers for Mg2SiO4
FMW = 140.691 # Formula molecular weight (g/cm3) for Mg2SiO4
# The following define the default initial state for material in the 201 table
R0REF = 3.227 # g/cm3 *** R0REF is inserted into the density array
K0REF = 1.336E12 # dynes/cm2 K0=rho0*cs0^2
T0REF = 298. # K -- *** T0REF is inserted into the temperature array
P0REF = 1.E6 # dynes/cm2 -- this defines the principal Hugoniot calculated below
IsaleEOS = extEOStable() # FIRST make new empty EOS object
IsaleEOS.loadextsesame(subdir+'NEW-SESAME-EXT.TXT') # LOAD THE EXTENDED 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
IsaleEOS.loadstdsesame(subdir+'NEW-SESAME-STD.TXT') # LOAD THE STANDARD 301 SESAME FILE GENERATED BY STSM VERSION OF ANEOS
IsaleEOS.MODELNAME = MODELNAME # string set above in user input
IsaleEOS.MDQ = np.zeros((IsaleEOS.NT,IsaleEOS.ND)) # makes the empty MDQ array
#print(IsaleEOS.units) # these are the default units for SESAME rho-T tables
#'Units: g/cm3, K, GPa, MJ/kg, MJ/kg, MJ/K/kg, cm/s, MJ/K/kg, KPA flag. 2D arrays are (NT,ND).'
# Add the header info to the table. This could be done during the loading.
# if made from this notebook, these values are set in the user-input above.
# ** MAKE SURE THEY MATCH ANEOS.INPUT **
IsaleEOS.MATID = MATID
IsaleEOS.DATE = DATE
IsaleEOS.VERSION = VERSION
IsaleEOS.FMN = FMN
IsaleEOS.FMW = FMW
IsaleEOS.R0REF = R0REF
IsaleEOS.K0REF = K0REF
IsaleEOS.T0REF = T0REF
IsaleEOS.P0REF = P0REF
#
# Load the information from ANEOS.INPUT and ANEOS.OUTPUT
IsaleEOS.loadaneos(aneosinfname=subdir+'ANEOS.INPUT',aneosoutfname=subdir+'ANEOS.OUTPUT',silent=True)
#
# calculate the principal Hugoniot from the table
IsaleEOS.calchugoniot(r0=IsaleEOS.R0REF,t0=IsaleEOS.T0REF)
#
# calculate the 1-bar profile; loop over temp
IsaleEOS.onebar.T = np.zeros(IsaleEOS.NT)
IsaleEOS.onebar.S = np.zeros(IsaleEOS.NT)
IsaleEOS.onebar.rho = np.zeros(IsaleEOS.NT)
it0 = np.where(IsaleEOS.T >= IsaleEOS.T0REF)[0]
id0 = np.arange(IsaleEOS.ND)#np.where(IsaleEOS.rho >= 0.8*IsaleEOS.R0REF)[0]
for iit in range(0,IsaleEOS.NT):
IsaleEOS.onebar.T[iit] = IsaleEOS.T[iit]
IsaleEOS.onebar.S[iit] = np.interp(1.E-4,IsaleEOS.P[iit,id0],IsaleEOS.S[iit,id0])
IsaleEOS.onebar.rho[iit] = np.interp(1.E-4,IsaleEOS.P[iit,id0],IsaleEOS.rho[id0])
#print(iit,IsaleEOS.onebar.rho[iit],IsaleEOS.onebar.T[iit],IsaleEOS.onebar.S[iit]*1.E3)
Figure 1 in Stewart et al., revised.¶
In [24]:
# colors for different data
colid = [0,.1,.3,.65,.80,.95]
labid = ['New ANEOS Hugoniot','Z fit Hugoniot','Gas gun Hugoniot','iSALE Hugoniot','GADGET+SPH-N Hugoniot','SPH-C+CTH Hugoniot','Tillotson Hugoniot']
labid2 = ['New ANEOS 1-bar','Z fit','Gas gun data','iSALE 1-bar','GADGET+SPH-N 1-bar','SPH-C+CTH 1-bar','Tillotson 1-bar']
linid = ['-','-','+','-','-','-']
thiid = [3,5,2,2,2,2]
msize = 3
labsize=18
#======================LOTS OF PLOTS============================
# plot the Hugoniots for comparison
sfont = 15
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14,10))
plt.subplots_adjust(wspace=0.25)
# make the line colors and such consistent across all the plots
style1 = ['-','blue',3,'Tabulated STP Hugoniot'] # eos table interpolated STP Hugoniot
style3 = ['-','red',3,'ANEOS Hugoniot'] # ANEOS Hugoniot returned from ANHUG in ANEOS.OUTPUT
style4 = ['-','orange',3,'ANEOS Liquid Hugoniot'] # ANEOS Hugoniot returned from ANHUG in ANEOS.OUTPUT for liquid initial conditions, stored as a file
#-------------
# A Density-Pressure Hugoniot
ai=0
aj=0
# Plot Tillotson
axes[ai,aj].plot(TillEOS.hug.rho,TillEOS.hug.P,'--',color='gray',label='Tillotson Hugoniot')
# plot old ANEOS
# iSALE ANEOS
col=local_cmaps.parula(colid[3])
axes[ai,aj].plot(IsaleEOS.hug.rho,IsaleEOS.hug.P,linid[3],color=col,markersize=msize,label=labid[3],linewidth=thiid[3])
# Gadget ANEOS
col=local_cmaps.parula(colid[4])
axes[ai,aj].plot(GadgetEOS.hug.rho,GadgetEOS.hug.P,linid[4],color=col,markersize=msize,label=labid[4],linewidth=thiid[4])
# Canup et al. 2013 parameters
col=local_cmaps.parula(colid[5])
axes[ai,aj].plot(CanupEOS.hug.rho,CanupEOS.hug.P,linid[5],color=col,markersize=msize,label=labid[5],linewidth=thiid[5])
#new ANEOS
axes[ai,aj].plot(NewEOS.hug.rho,NewEOS.hug.P,style1[0],color='black',markersize=style1[2],label=labid[0],linewidth=thiid[0])
# plot data on top
# QMD points Root et al. 2013
axes[ai,aj].plot(QMDH_r[1::],QMDH_p[1::],'x',markersize=6,color='darkred',label='QMD')
# Z data points Root et al. 2013
col=local_cmaps.parula(colid[1])
axes[ai,aj].errorbar(Zdat_r,Zdat_p,xerr=Zdat_rerr, yerr=Zdat_perr,fmt='o', label="Z data", color=col, elinewidth=1)
# gas gun data Mosenfelder et al. 2007
col=local_cmaps.parula(colid[2])
axes[ai,aj].plot(LowHugDat_r,LowHugDat_p,'+',color=col,label='Gas gun data')
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(0,1100)
axes[ai,aj].set_xlim(3.,8.)
axes[ai,aj].text(7.5, 100, 'A', fontsize=labsize)
axes[ai,aj].legend(fontsize=sfont-5)
#-------------
# B pressure - temperature Hugoniots
ai=0
aj=1
# plot old Hugoniots first
col=local_cmaps.parula(colid[3])
axes[ai,aj].plot(IsaleEOS.hug.P,IsaleEOS.hug.T/1.E3,linid[3],color=col,markersize=msize,label=labid[3],linewidth=thiid[3])
col=local_cmaps.parula(colid[4])
axes[ai,aj].plot(GadgetEOS.hug.P,GadgetEOS.hug.T/1.e3,linid[4],color=col,markersize=msize,label=labid[4],linewidth=thiid[4])
col=local_cmaps.parula(colid[5])
axes[ai,aj].plot(CanupEOS.hug.P,CanupEOS.hug.T/1.e3,linid[5],color=col,markersize=msize,label=labid[5],linewidth=thiid[5])
# plot omega bands
#####OMEGA data from Root et al. 2018
col=local_cmaps.parula(0.5)
axes[ai,aj].fill_between(OM_D1P*1000,(OM_DT1-OM_DTe1)/1000,(OM_DT1+OM_DTe1)/1000,label="OMEGA data",
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D2P*1000,(OM_DT2-OM_DTe2)/1000,(OM_DT2+OM_DTe2)/1000,
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D3P*1000,(OM_DT3-OM_DTe3)/1000,(OM_DT3+OM_DTe3)/1000,
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D4P*1000,(OM_DT4-OM_DTe4)/1000,(OM_DT4+OM_DTe4)/1000,
color=col,alpha=0.25)
#new ANEOS Hugoniot
axes[ai,aj].plot(NewEOS.hug.P,NewEOS.hug.T/1.e3,style1[0],color='black',markersize=style1[2],label=labid[0],linewidth=thiid[0])
#Z data on top
col=local_cmaps.parula(colid[1])
axes[ai,aj].errorbar(ZTdat_p,ZTdat_t/1.E3,xerr=ZTdat_perr,yerr=ZTdat_terr/1.E3,fmt='o',color=col,label="Z data",elinewidth=1)
# QMD points
axes[ai,aj].plot(QMDH_p[1::],QMDH_t[1::]/1.E3,'x',markersize=6,color='darkred',label='QMD')
axes[ai,aj].set_xlim(200,1100)
axes[ai,aj].set_ylim(4,45)
axes[ai,aj].text(1000, 7.5, 'B', fontsize=labsize)
axes[ai,aj].set_ylabel('Temperature (1000 K)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].legend(fontsize=sfont-5)
#-------------
# C Pressure - Sp. Entropy Hugoniots
ai=1
aj=0
col=local_cmaps.parula(colid[1])
axes[ai,aj].plot(Zfit_p,Zfit_s*1.E3,'-',linewidth=thiid[1],color=col,label='Calculated Hugoniot')
axes[ai,aj].fill_between(Zfit_p,(Zfit_s-Zfit_serr)*1000.,(Zfit_s+Zfit_serr)*1000.,color=col,alpha=0.2)
# Tie point from Davies et al. 2019
#axes[ai,aj].errorbar(Ztie_p,Ztie_s*1.E3,xerr=Ztie_perr,yerr=Ztie_serr*1.E3,fmt='o',markersize=5,color='red',label='Entropy Tie Point (Davies et al. 2019)',elinewidth=3)
col=local_cmaps.parula(colid[3])
axes[ai,aj].plot(IsaleEOS.hug.P,IsaleEOS.hug.S*1.e3,linid[3],color=col,markersize=msize,label=labid[3],linewidth=thiid[3])
col=local_cmaps.parula(colid[4])
axes[ai,aj].plot(GadgetEOS.hug.P,GadgetEOS.hug.S*1.e3,linid[4],color=col,markersize=msize,label=labid[4],linewidth=thiid[4])
col=local_cmaps.parula(colid[5])
axes[ai,aj].plot(CanupEOS.hug.P,CanupEOS.hug.S*1.e3,linid[5],color=col,markersize=msize,label=labid[5],linewidth=thiid[5])
#new
axes[ai,aj].plot(NewEOS.hug.P,NewEOS.hug.S*1.e3,style1[0],color='black',markersize=style1[2],label=labid[0],linewidth=thiid[0])
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(2,7.5)
axes[ai,aj].set_xlim(100,1000)
axes[ai,aj].text(900, 2.5, 'C', fontsize=labsize)
axes[ai,aj].legend(fontsize=sfont-5)
#-----
# D Temperature - Sp. Entropy at 1 bar
ai=1
aj=1
#isale
col=local_cmaps.parula(colid[3])
tmp = np.where((IsaleEOS.onebar.S <= IsaleEOS.onebar.Sim)&(IsaleEOS.onebar.S > 0.))[0]
axes[ai,aj].plot(IsaleEOS.onebar.T[tmp],IsaleEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,linewidth=thiid[3]+2)
tmp = np.where((IsaleEOS.onebar.S >= IsaleEOS.onebar.Scm)&(IsaleEOS.onebar.S <= IsaleEOS.onebar.Siv))[0]
axes[ai,aj].plot(IsaleEOS.onebar.T[tmp],IsaleEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,linewidth=thiid[3]+2)
tmp = np.where((IsaleEOS.onebar.S >= IsaleEOS.onebar.Scv))[0]
axes[ai,aj].plot(IsaleEOS.onebar.T[tmp],IsaleEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,label=labid2[3],linewidth=thiid[3]+2)
#gadget
col=local_cmaps.parula(colid[4])
tmp = np.where((GadgetEOS.onebar.S <= GadgetEOS.onebar.Sim)&(GadgetEOS.onebar.S > 0.))[0]
axes[ai,aj].plot(GadgetEOS.onebar.T[tmp],GadgetEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,linewidth=thiid[4])
tmp = np.where((GadgetEOS.onebar.S >= GadgetEOS.onebar.Scm)&(GadgetEOS.onebar.S <= GadgetEOS.onebar.Siv))[0]
axes[ai,aj].plot(GadgetEOS.onebar.T[tmp],GadgetEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,linewidth=thiid[4])
tmp = np.where((GadgetEOS.onebar.S >= GadgetEOS.onebar.Scv))[0]
axes[ai,aj].plot(GadgetEOS.onebar.T[tmp],GadgetEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,label=labid2[4],linewidth=thiid[4])
#canup
col=local_cmaps.parula(colid[5])
tmp = np.where((CanupEOS.onebar.S <= CanupEOS.onebar.Sim)&(CanupEOS.onebar.S > 0.))[0]
axes[ai,aj].plot(CanupEOS.onebar.T[tmp],CanupEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,linewidth=thiid[5])
tmp = np.where((CanupEOS.onebar.S >= CanupEOS.onebar.Scm)&(CanupEOS.onebar.S <= CanupEOS.onebar.Siv))[0]
axes[ai,aj].plot(CanupEOS.onebar.T[tmp],CanupEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,linewidth=thiid[5])
tmp = np.where((CanupEOS.onebar.S >= CanupEOS.onebar.Scv))[0]
axes[ai,aj].plot(CanupEOS.onebar.T[tmp],CanupEOS.onebar.S[tmp]*1.e3,'-',color=col,markersize=msize,label=labid2[5],linewidth=thiid[5])
# Plot one bar specific entropy by integrating the specific heat capacity
col=local_cmaps.parula(.1)
axes[ai,aj].plot(Gilletdatarr.iloc[:,0].values,Gilletdatarr.iloc[:,1].values/1.e3,linestyle='-',color=col,linewidth=6,label='Solid 1-bar data')
col=local_cmaps.parula(.3)
# calculate constant Cv heat capacity in the liquid
sintliq = np.zeros(int(NewEOS.onebar.Tvap-NewEOS.onebar.Tmelt)+1)
sintliq[0]=NewEOS.onebar.Scm*1.e3
tintliq = np.arange(NewEOS.onebar.Tvap-NewEOS.onebar.Tmelt)+NewEOS.onebar.Tmelt
it=0
for tt in tintliq:
sintliq[it] = NewEOS.onebar.Scm*1.e6 + 1926.18*np.log(tt/NewEOS.onebar.Tmelt) # J/K/kg
it=it+1
axes[ai,aj].plot(tintliq,sintliq/1.e3,linestyle='-',color=col,linewidth=6,label='Liquid 1-bar data')
# Plot New ANEOS model
#axes[ai,aj].plot(NewEOS.onebar.T,NewEOS.onebar.S*1.e3,'+',color='blue',label="ANEOS 1 bar")
tmp = np.where((NewEOS.onebar.S <= NewEOS.onebar.Sim)&(NewEOS.onebar.S > 0.))
axes[ai,aj].plot(NewEOS.onebar.T[tmp],NewEOS.onebar.S[tmp]*1.e3,'-',color='black',markersize=style1[2],linewidth=thiid[0],label=labid2[0])
tmp = np.where((NewEOS.onebar.S >= NewEOS.onebar.Scm)&(NewEOS.onebar.S <= NewEOS.onebar.Siv))
axes[ai,aj].plot(NewEOS.onebar.T[tmp],NewEOS.onebar.S[tmp]*1.e3,'-',color='black',markersize=style1[2],linewidth=thiid[0])
tmp = np.where((NewEOS.onebar.S >= NewEOS.onebar.Scv))
axes[ai,aj].plot(NewEOS.onebar.T[tmp],NewEOS.onebar.S[tmp]*1.e3,'-',color='black',markersize=style1[2],linewidth=thiid[0])
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_xlabel('Temperature (K)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(0,11)
axes[ai,aj].set_xlim(0,5000)
axes[ai,aj].text(4450, 1, 'D', fontsize=labsize)
axes[ai,aj].legend(fontsize=sfont-5)
plt.tight_layout(pad=0.6)
plt.savefig('Stewart-etal-2019-Fig1-CompareHugoniots.pdf', format='pdf', dpi=1000,transparent=True)
Figure 2 in Stewart et al., revised.¶
In [25]:
# make the line colors and such consistent across all the plots
style1 = ['-','blue',3,'Tabulated STP Hugoniot'] # eos table interpolated STP Hugoniot
#style2 = ['--','blue',3,'Tabulated Porous Hugoniot'] # eos table interpolated porous Hugoniot
style3 = ['-','red',3,'ANEOS Hugoniot'] # ANEOS Hugoniot returned from ANHUG in ANEOS.OUTPUT
style4 = ['-','orange',3,'ANEOS Liquid Hugoniot'] # ANEOS Hugoniot returned from ANHUG in ANEOS.OUTPUT for liquid initial conditions, stored as a file
#
#
#======================LOTS OF PLOTS============================
# Plot aneos phase boundaries with focus on the vapor curve
sfont = 15
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14,10))
plt.subplots_adjust(wspace=0.25)
coltil="darkgrey"
dskip=10
relthick=4
# gather boundaries for the E-P box of the interpolated region in the Tillotson EOS
# (dens < tilleos[r0]) and (eng < tilleos[ECV] and (eng > tilleos[EIV]))
zzz1 = np.where(TillEOS.U > olivinetill[2]/1.e6)
zzz2 = np.where(TillEOS.U < olivinetill[3]/1.e6)
tillintpmaxarr = np.zeros(max(zzz2[0])-min(zzz1[0]))
tillintpminarr = np.zeros(max(zzz2[0])-min(zzz1[0]))
tillintpminarr[:]=1.e-16 # GPa
tillintearr = np.zeros(max(zzz2[0])-min(zzz1[0]))
iiie=0
for iie in range(min(zzz1[0]),max(zzz2[0])):
zzz3 = np.where(TillEOS.rho < olivinetill[0]/1.e3)
#print(iie,till2earr[iie],max(till2parr[iie,zzz3[0]]))
#axes[ai,aj].plot(till2earr[iie],max(till2parr[iie,zzz3[0]]),'o',color='black')
tillintpmaxarr[iiie]=max(TillEOS.P[iie,zzz3[0]])
tillintearr[iiie]=TillEOS.U[iie]
iiie=iiie+1
#-------
#A. ANEOS Sp. Energy - pressure with isochores
ai=0
aj=0
# plot colored isochores
logdcolmin=-15
logdcolmax=-0.3
for iid in range(0,NewEOS.ND-1,dskip):
if NewEOS.rho[iid] < 0.5:
icolscale = (np.log10(NewEOS.rho[iid])-logdcolmin)/(logdcolmax-logdcolmin)*0.6
if icolscale > 0.6:
icolscale=0.6
if icolscale < 0:
icolscale=0
else:
icolscale = (NewEOS.rho[iid]-0.5)/(5-0.5)*0.4+0.6
if icolscale > 1.:
icolscale=1.
if icolscale < 0.6:
icolscale=0.6
col=local_cmaps.parula(icolscale)
#print(iid,andarr[iid],np.log10(andarr[iid]),icolscale)
axes[ai,aj].loglog(NewEOS.U[:,iid],NewEOS.P[:,iid],'o',markersize=2,color=col)
# Plot aneos phase boundaries over the isochores
tmp = np.where((NewEOS.vc.Pl > 1.E-13)&(NewEOS.vc.T < NewEOS.tp.T))[0] # GPa
axes[ai,aj].plot(NewEOS.vc.Ul[tmp],NewEOS.vc.Pl[tmp],styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
tmp = np.where((NewEOS.vc.Pl >= NewEOS.tp.P)&(NewEOS.vc.T >= NewEOS.tp.T))[0]
axes[ai,aj].plot(NewEOS.vc.Ul[tmp],NewEOS.vc.Pl[tmp],styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.vc.Uv,NewEOS.vc.Pv,styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.cp.U,NewEOS.cp.P,'o',color=stylephasept[1],markersize=stylephasept[2])
if NewEOS.tp.T > 0:
tmp = np.where(NewEOS.mc.Pl > 0.)[0] # GPa
axes[ai,aj].plot(NewEOS.mc.Ul[tmp],np.append(NewEOS.tp.P,NewEOS.mc.Pl[tmp[1::]]),styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.mc.Us[tmp],np.append(NewEOS.tp.P,NewEOS.mc.Ps[tmp[1::]]),styleanphase[0],color=styleanphase[1],linewidth=styleanphase[2])
axes[ai,aj].plot([NewEOS.mc.Us[tmp[0]],np.interp(NewEOS.tp.P,NewEOS.vc.Pv,NewEOS.vc.Uv)],[NewEOS.tp.P,NewEOS.tp.P],'-',color='black',linewidth=2)
axes[ai,aj].set_ylim(1.e-18,1000.)
axes[ai,aj].set_xlim(1,40.)
axes[ai,aj].text(1.1,1.e-3,'A. ANEOS',fontsize=labsize)
axes[ai,aj].set_xlabel('Specific Internal Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
labsize2=14
axes[ai,aj].text(2.1,1.e-6,'S',fontsize=labsize2)
axes[ai,aj].text(2.9,1.e-6,'S+L',fontsize=labsize2)
axes[ai,aj].text(4.05,1.e-6,'L',fontsize=labsize2)
axes[ai,aj].text(12,1.e-6,'L+V',fontsize=labsize2)
axes[ai,aj].text(25,1.e-6,'V',fontsize=labsize2)
axes[ai,aj].text(12,1.e-12,'S+V',fontsize=labsize2)
# no legend
#axes[ai,aj].legend(fontsize=sfont-5)
#-------
# B sp. internal energy vs. pressure Tillotson isochores
ai=0
aj=1
logdcolmin=-15
logdcolmax=-0.3
for iid in range(0,TillEOS.ND-1,dskip):
if TillEOS.rho[iid] < 0.5:
icolscale = (np.log10(TillEOS.rho[iid])-logdcolmin)/(logdcolmax-logdcolmin)*0.6
if icolscale > 0.6:
icolscale=0.6
if icolscale < 0:
icolscale=0
else:
icolscale = (TillEOS.rho[iid]-0.5)/(5-0.5)*0.4+0.6
if icolscale > 1.:
icolscale=1.
if icolscale < 0.6:
icolscale=0.6
col=local_cmaps.parula(icolscale)
axes[ai,aj].loglog(TillEOS.U,TillEOS.P[:,iid],'o',markersize=2,color=col)
# Plot aneos phase boundaries over the isochores
tmp = np.where((NewEOS.vc.Pl > 1.E-13)&(NewEOS.vc.T < NewEOS.tp.T))[0] # GPa
axes[ai,aj].plot(NewEOS.vc.Ul[tmp],NewEOS.vc.Pl[tmp],styleanphase[0],color=coltil,linewidth=styleanphase[2])
tmp = np.where((NewEOS.vc.Pl >= NewEOS.tp.P)&(NewEOS.vc.T >= NewEOS.tp.T))[0]
axes[ai,aj].plot(NewEOS.vc.Ul[tmp],NewEOS.vc.Pl[tmp],styleanphase[0],color=coltil,linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.vc.Uv,NewEOS.vc.Pv,styleanphase[0],color=coltil,linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.cp.U,NewEOS.cp.P,'o',color=coltil,markersize=stylephasept[2])
if NewEOS.tp.T > 0:
tmp = np.where(NewEOS.mc.Pl > 0.)[0] # GPa
axes[ai,aj].plot(NewEOS.mc.Ul[tmp],np.append(NewEOS.tp.P,NewEOS.mc.Pl[tmp[1::]]),styleanphase[0],color=coltil,linewidth=styleanphase[2])
axes[ai,aj].plot(NewEOS.mc.Us[tmp],np.append(NewEOS.tp.P,NewEOS.mc.Ps[tmp[1::]]),styleanphase[0],color=coltil,linewidth=styleanphase[2])
axes[ai,aj].plot([NewEOS.mc.Us[tmp[0]],np.interp(NewEOS.tp.P,NewEOS.vc.Pv,NewEOS.vc.Uv)],[NewEOS.tp.P,NewEOS.tp.P],'-',color=coltil,linewidth=2)
# draw a box around the interpolated region
axes[ai,aj].plot(tillintearr,tillintpmaxarr,'-',color='black')
axes[ai,aj].plot(tillintearr,tillintpminarr,'-',color='black')
axes[ai,aj].plot([min(tillintearr),min(tillintearr)],[1.e-16,min(tillintpmaxarr)],'-',color='black')
axes[ai,aj].plot([max(tillintearr),max(tillintearr)],[1.e-16,max(tillintpmaxarr)],'-',color='black')
axes[ai,aj].set_ylim(1.e-18,1000.)
axes[ai,aj].set_xlim(1,40.)
axes[ai,aj].set_xlabel('Specific Internal Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].text(1.1,1.e-3,'B. Tillotson',fontsize=labsize)
# no legend
#axes[ai,aj].legend(fontsize=sfont-5)
#--------------------------
# COMPARE ISENTROPES BETWEEN TILLOTSON AND ANEOS STARTING FROM NEAR 500 GPa
#
ptarget = 500.0 # GPa
# first extract the isentropes for the planet from the EOS tables
TillIsen = isentrope_class() # code in eostable.py
TillIsen.density = np.zeros(TillEOS.ND)
TillIsen.pressure = np.zeros(TillEOS.ND)
TillIsen.energy = np.zeros(TillEOS.ND)
TillIsen.soundspeed = np.zeros(TillEOS.ND)
TillIsen.partvel = np.zeros(TillEOS.ND)
TillIsen.region = np.zeros(TillEOS.ND)
# Tillotson Isentrope in MKS units
rhug = np.interp(ptarget,TillEOS.hug.P,TillEOS.hug.rho) # g/cm3
irh=int(np.round(np.where(TillEOS.hug.rho >= rhug)[0][0])) # find closest larger density
ir0=int(np.round(np.where(TillEOS.rho == TillEOS.hug.rho[irh])[0][0])) # find closest larger density
TillIsen.density = np.copy(TillEOS.rho)*1.E3 # kg/m3 # begin with a density exactly on the grid
TillIsen.pressure[ir0] = TillEOS.hug.P[irh]*1.e9 # Pa
TillIsen.energy[ir0] = TillEOS.hug.U[irh] # MJ/kg
TillIsen.partvel[ir0] = TillEOS.hug.up[irh]*1.E3 # m/s
TillIsen.soundspeed[ir0] = TillEOS.hug.cs[irh]*1.E3 # m/s
TillIsen.region[ir0] = 1 # compressed region
print('Tillotson Hugoniot starting pressure:',TillIsen.pressure[ir0]/1.e9)
#print('Tillotson Hugoniot starting point:')
#print('irh, P, rho, E, up, cs: ',ir0,TillIsen.pressure[ir0],TillIsen.density[ir0],TillIsen.energy[ir0],TillIsen.partvel[ir0],TillIsen.soundspeed[ir0])
plast = TillIsen.pressure[ir0] # Pa
uplast = TillIsen.partvel[ir0] # m/s
cslast = TillIsen.soundspeed[ir0] # m/s
elast = TillIsen.energy[ir0] #MJ/kg
for iir in range(ir0-1,0,-1): # step down from Hugoniot density to the lowest density in the table
dp = cslast*cslast*(TillIsen.density[iir+1]-TillIsen.density[iir]) # Pa
pnew = (plast - dp) # Pa
enew = np.interp(pnew,TillEOS.P[:,iir]*1.E9,TillEOS.U) # MJ/kg
csnew = np.interp(pnew,TillEOS.P[:,iir]*1.E9,TillEOS.cs[:,iir])*1.E3 # km/s -> m/s
upnew = uplast + dp/(TillIsen.density[iir]*cslast) # m/s
TillIsen.pressure[iir] = pnew # Pa
TillIsen.energy[iir] = enew # MJ/kg
TillIsen.partvel[iir] = upnew # m/s
TillIsen.soundspeed[iir] = csnew # m/s
eind = int(np.round(np.where(TillEOS.U >= enew)[0][0]))
TillIsen.region[iir] = TillEOS.region[eind,iir]
#if pnew>0:
# print('iir, P, rho, E, up, cs, reg: ',iir,pnew/1.e9,TillIsen.density[iir]/1.e3,enew,upnew,csnew,TillIsen.region[iir])
plast = pnew
uplast = upnew
cslast = csnew
# plot tillotson isentrope
ai=0
aj=1
indtillcs = np.where((TillIsen.region == 1)&(TillIsen.pressure > 0.))
indtillcs2 = np.where((TillIsen.region == 2) & (TillIsen.pressure > 0.))
axes[ai,aj].plot(TillIsen.energy[indtillcs],TillIsen.pressure[indtillcs]/1.e9,'-',color='red',linewidth=relthick)
axes[ai,aj].plot(TillIsen.energy[indtillcs2],TillIsen.pressure[indtillcs2]/1.e9,'-',color='red',linewidth=1)
# ANEOS ISENTROPE NEAR SAME PRESSURE
ANEOSIsen = isentrope_class() # code in eostable.py
Sisen = np.interp(ptarget,NewEOS.hug.P,NewEOS.hug.S) # MJ/K/kg
# loop across all densities and extract the values for the requested isentrope
for i in range(0,NewEOS.ND):
ind = np.where((NewEOS.S[:,i] > 0))[0]
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.P[ind,i]) # MJ/K/kg, GPa
ANEOSIsen.pressure = np.append(ANEOSIsen.pressure,interpfunction(Sisen)) # GPa
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.T[ind]) # MJ/K/kg, GPa
ANEOSIsen.temperature = np.append(ANEOSIsen.temperature,interpfunction(Sisen)) # GPa
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.cs[ind,i]) # MJ/K/kg, cm/s
ANEOSIsen.soundspeed = np.append(ANEOSIsen.soundspeed,interpfunction(Sisen)) # cm/s
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.U[ind,i]) # MJ/K/kg, MJ/kg
ANEOSIsen.energy = np.append(ANEOSIsen.energy,interpfunction(Sisen)) # MJ/kg
ANEOSIsen.density = np.copy(NewEOS.rho) # g/cm3
ANEOSIsen.partvel = np.zeros(NewEOS.ND) # m/s
ir0 = int(np.round(np.where(ANEOSIsen.pressure >= ptarget)[0][0])) # go up just past the intersection with Hugoniot
ANEOSIsen.partvel[ir0] = np.interp(ptarget,NewEOS.hug.P,NewEOS.hug.up)*1.E3 # m/s
print('ANEOS Starting Pressure:',ptarget)# using the actual isentrope at ptarget ANEOSIsen.pressure[ir0])
for iir in range (ir0-1,0,-1):
dp = (ANEOSIsen.pressure[iir+1]-ANEOSIsen.pressure[iir])*1.E9 # Pa
ANEOSIsen.partvel[iir] = ANEOSIsen.partvel[iir+1] + dp/(TillIsen.density[iir]*ANEOSIsen.soundspeed[iir+1]/1.E2) # m/s
#print(iir,ANEOSIsen.pressure[iir],ANEOSIsen.partvel[iir],dp,TillIsen.density[iir])
# plot aneos isentrope
ai=0
aj=0
tmp = np.where(ANEOSIsen.pressure < ptarget)[0]
axes[ai,aj].plot(ANEOSIsen.energy[tmp],ANEOSIsen.pressure[tmp],'-',color='blue',linewidth=relthick)
#------- plot rho vs. P
# C. density vs. Pressure release paths
ai=1
aj=0
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(1.e-9,1000)
axes[ai,aj].set_xlim(1.e-9,10)
axes[ai,aj].text(0.2e-8,0.5e-8,'C',fontsize=labsize)
axes[ai,aj].plot(TillEOS.hug.rho,TillEOS.hug.P,color='grey',label='Tillotson Hugoniot')
axes[ai,aj].loglog(NewEOS.hug.rho,NewEOS.hug.P,style1[0],color='black',markersize=style1[2],label='ANEOS Hugoniot')
indtillcs = np.where((TillIsen.region == 1)&(TillIsen.pressure > 0.))
indtillcs2 = np.where((TillIsen.region == 2) & (TillIsen.pressure > 0.))
axes[ai,aj].plot(TillIsen.density[indtillcs]/1.e3,TillIsen.pressure[indtillcs]/1.e9,'-',color='red',linewidth=relthick,label='Tillotson release 500 GPa')
axes[ai,aj].plot(TillIsen.density[indtillcs2]/1.e3,TillIsen.pressure[indtillcs2]/1.e9,'-',color='red',linewidth=1)
tmp = np.where(ANEOSIsen.pressure < ptarget)[0]
axes[ai,aj].plot(ANEOSIsen.density[tmp],ANEOSIsen.pressure[tmp],'-',color='blue',linewidth=relthick,label='ANEOS release 500 GPa')
axes[ai,aj].legend(fontsize=sfont-5)
#------- plot Up vs. P
ai=1
aj=1
axes[ai,aj].set_xlabel('Particle Velocity (km/s)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(1.e-9,1000)
axes[ai,aj].set_xlim(5,30)
axes[ai,aj].text(6,0.5e-8,'D',fontsize=labsize)
axes[ai,aj].semilogy(TillEOS.hug.up,TillEOS.hug.P,color='grey',label='Tillotson Hugoniot')
axes[ai,aj].semilogy(NewEOS.hug.up,NewEOS.hug.P,style1[0],color='black',markersize=style1[2],label='ANEOS Hugoniot')
indtillcs = np.where((TillIsen.region == 1)&(TillIsen.pressure > 0.))
indtillcs2 = np.where((TillIsen.region == 2) & (TillIsen.pressure > 0.))
axes[ai,aj].plot(TillIsen.partvel[indtillcs]/1.e3,TillIsen.pressure[indtillcs]/1.e9,'-',color='red',linewidth=relthick,label='Tillotson release 500 GPa')
axes[ai,aj].plot(TillIsen.partvel[indtillcs2]/1.e3,TillIsen.pressure[indtillcs2]/1.e9,'-',color='red',linewidth=1)
tmp =np.where(ANEOSIsen.partvel > 0.)[0]
axes[ai,aj].semilogy(ANEOSIsen.partvel[tmp]/1.e3,ANEOSIsen.pressure[tmp],'-',color='blue',linewidth=relthick,label='ANEOS release 500 GPa')
#axes[ai,aj].set_title("Release from 500 GPa")
#--------------------------
# COMPARE ISENTROPES BETWEEN TILLOTSON AND ANEOS STARTING FROM NEAR 200 GPa
#
#
ptarget = 200.0 # GPa
# first extract the isentropes for the planet from the EOS tables
TillIsen = isentrope_class() # code in eostable.py
TillIsen.density = np.zeros(TillEOS.ND)
TillIsen.pressure = np.zeros(TillEOS.ND)
TillIsen.energy = np.zeros(TillEOS.ND)
TillIsen.soundspeed = np.zeros(TillEOS.ND)
TillIsen.partvel = np.zeros(TillEOS.ND)
TillIsen.region = np.zeros(TillEOS.ND)
# Tillotson Isentrope in MKS units
rhug = np.interp(ptarget,TillEOS.hug.P,TillEOS.hug.rho) # g/cm3
irh=int(np.round(np.where(TillEOS.hug.rho >= rhug)[0][0])) # find closest larger density
ir0=int(np.round(np.where(TillEOS.rho == TillEOS.hug.rho[irh])[0][0])) # find closest larger density
TillIsen.density = np.copy(TillEOS.rho)*1.E3 # kg/m3 # begin with a density exactly on the grid
TillIsen.pressure[ir0] = TillEOS.hug.P[irh]*1.e9 # Pa
TillIsen.energy[ir0] = TillEOS.hug.U[irh] # MJ/kg
TillIsen.partvel[ir0] = TillEOS.hug.up[irh]*1.E3 # m/s
TillIsen.soundspeed[ir0] = TillEOS.hug.cs[irh]*1.E3 # m/s
TillIsen.region[ir0] = 1 # compressed region
print('Tillotson Hugoniot starting pressure:',TillIsen.pressure[ir0]/1.e9)
#print('irh, P, rho, E, up, cs: ',ir0,TillIsen.pressure[ir0],TillIsen.density[ir0],TillIsen.energy[ir0],TillIsen.partvel[ir0],TillIsen.soundspeed[ir0])
plast = TillIsen.pressure[ir0] # Pa
uplast = TillIsen.partvel[ir0] # m/s
cslast = TillIsen.soundspeed[ir0] # m/s
elast = TillIsen.energy[ir0] #MJ/kg
for iir in range(ir0-1,0,-1): # step down from Hugoniot density to the lowest density in the table
dp = cslast*cslast*(TillIsen.density[iir+1]-TillIsen.density[iir]) # Pa
pnew = (plast - dp) # Pa
enew = np.interp(pnew,TillEOS.P[:,iir]*1.E9,TillEOS.U) # MJ/kg
csnew = np.interp(pnew,TillEOS.P[:,iir]*1.E9,TillEOS.cs[:,iir])*1.E3 # km/s -> m/s
upnew = uplast + dp/(TillIsen.density[iir]*cslast) # m/s
TillIsen.pressure[iir] = pnew # Pa
TillIsen.energy[iir] = enew # MJ/kg
TillIsen.partvel[iir] = upnew # m/s
TillIsen.soundspeed[iir] = csnew # m/s
eind = int(np.round(np.where(TillEOS.U >= enew)[0][0]))
TillIsen.region[iir] = TillEOS.region[eind,iir]
#if pnew>0:
# print('iir, P, rho, E, up, cs, reg: ',iir,pnew/1.e9,TillIsen.density[iir]/1.e3,enew,upnew,csnew,TillIsen.region[iir])
plast = pnew
uplast = upnew
cslast = csnew
# plot tillotson isentrope
ai=0
aj=1
indtillcs = np.where((TillIsen.region == 1)&(TillIsen.pressure > 0.))
indtillcs2 = np.where((TillIsen.region == 2) & (TillIsen.pressure > 0.))
axes[ai,aj].plot(TillIsen.energy[indtillcs],TillIsen.pressure[indtillcs]/1.e9,':',color='red',linewidth=relthick)
axes[ai,aj].plot(TillIsen.energy[indtillcs2],TillIsen.pressure[indtillcs2]/1.e9,':',color='red',linewidth=1)
# ANEOS ISENTROPE NEAR SAME PRESSURE
ANEOSIsen = isentrope_class() # code in eostable.py
Sisen = np.interp(ptarget,NewEOS.hug.P,NewEOS.hug.S) # MJ/K/kg
# loop across all densities and extract the values for the requested isentrope
for i in range(0,NewEOS.ND):
ind = np.where((NewEOS.S[:,i] > 0))[0]
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.P[ind,i]) # MJ/K/kg, GPa
ANEOSIsen.pressure = np.append(ANEOSIsen.pressure,interpfunction(Sisen)) # GPa
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.T[ind]) # MJ/K/kg, GPa
ANEOSIsen.temperature = np.append(ANEOSIsen.temperature,interpfunction(Sisen)) # GPa
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.cs[ind,i]) # MJ/K/kg, cm/s
ANEOSIsen.soundspeed = np.append(ANEOSIsen.soundspeed,interpfunction(Sisen)) # cm/s
interpfunction = interpolate.interp1d(NewEOS.S[ind,i],NewEOS.U[ind,i]) # MJ/K/kg, MJ/kg
ANEOSIsen.energy = np.append(ANEOSIsen.energy,interpfunction(Sisen)) # MJ/kg
ANEOSIsen.density = np.copy(NewEOS.rho) # g/cm3
ANEOSIsen.partvel = np.zeros(NewEOS.ND) # m/s
ir0 = int(np.round(np.where(ANEOSIsen.pressure >= ptarget)[0][0])) # go up just past the intersection with Hugoniot
ANEOSIsen.partvel[ir0] = np.interp(ptarget,NewEOS.hug.P,NewEOS.hug.up)*1.E3 # m/s
print('ANEOS Starting Pressure:',ptarget)# using the actual isentrope at ptarget ANEOSIsen.pressure[ir0])
for iir in range (ir0-1,0,-1):
dp = (ANEOSIsen.pressure[iir+1]-ANEOSIsen.pressure[iir])*1.E9 # Pa
ANEOSIsen.partvel[iir] = ANEOSIsen.partvel[iir+1] + dp/(TillIsen.density[iir]*ANEOSIsen.soundspeed[iir+1]/1.E2) # m/s
#print(iir,ANEOSIsen.pressure[iir],ANEOSIsen.partvel[iir],dp,TillIsen.density[iir])
# plot aneos isentrope
ai=0
aj=0
tmp = np.where(ANEOSIsen.pressure < ptarget)[0]
axes[ai,aj].plot(ANEOSIsen.energy[tmp],ANEOSIsen.pressure[tmp],':',color='blue',linewidth=relthick)
## plot density-pressure
ai=1
aj=0
indtillcs = np.where((TillIsen.region == 1)&(TillIsen.pressure > 0.))
indtillcs2 = np.where((TillIsen.region == 2) & (TillIsen.pressure > 0.))
axes[ai,aj].plot(TillIsen.density[indtillcs]/1.e3,TillIsen.pressure[indtillcs]/1.e9,':',color='red',linewidth=relthick,label='Tillotson release 200 GPa')
axes[ai,aj].plot(TillIsen.density[indtillcs2]/1.e3,TillIsen.pressure[indtillcs2]/1.e9,':',color='red',linewidth=1)
tmp = np.where(ANEOSIsen.pressure < ptarget)[0]
axes[ai,aj].plot(ANEOSIsen.density[tmp],ANEOSIsen.pressure[tmp],':',color='blue',linewidth=relthick,label='ANEOS release 200 GPa')
ai=1
aj=1
indtillcs = np.where((TillIsen.region == 1)&(TillIsen.pressure > 0.))
indtillcs2 = np.where((TillIsen.region == 2) & (TillIsen.pressure > 0.))
axes[ai,aj].plot(TillIsen.partvel[indtillcs]/1.e3,TillIsen.pressure[indtillcs]/1.e9,':',color='red',linewidth=relthick,label='Tillotson release 200 GPa')
axes[ai,aj].plot(TillIsen.partvel[indtillcs2]/1.e3,TillIsen.pressure[indtillcs2]/1.e9,':',color='red',linewidth=1)
tmp =np.where(ANEOSIsen.partvel > 0.)[0]
axes[ai,aj].semilogy(ANEOSIsen.partvel[tmp]/1.e3,ANEOSIsen.pressure[tmp],':',color='blue',linewidth=relthick,label='ANEOS release 200 GPa')
axes[1,0].legend(fontsize=sfont-5)
axes[1,1].legend(fontsize=sfont-5)
plt.tight_layout(pad=0.6)
plt.savefig('Stewart-etal-2019-Fig2-CompareTillotson.pdf', format='pdf', dpi=1000,transparent=True)
In [ ]:
Comparison of phase boundaries between different forsterite ANEOS models¶
Phase boundaries shown with solid lines. Hugoniots shown with dashed lines.
Only the iSALE and New ANEOS models have melt curves. New ANEOS does not have a high-pressure phase transition, but the other models do.
In [26]:
# PHASE DIAGRAM PLOTS
labid3 = ['New ANEOS','Z fit','Gas gun data','iSALE ANEOS','GADGET+SPH-N ANEOS','SPH-C+CTH ANEOS','Tillotson']
#======================LOTS OF PLOTS============================
# Plot aneos phase boundaries with focus on the vapor curve
sfont = 15
fig, axes = plt.subplots(nrows=4, ncols=2, figsize=(14,24))
plt.subplots_adjust(wspace=0.5)
#------------------------------
# entropy-temperature
ai=0
aj=0
#col=local_cmaps.parula(colid[4])
#axes[ai,aj].plot(GadgetEOS.hug.P,GadgetEOS.hug.S*1.e3,linid[4],color=col,markersize=msize,label=labid[4],linewidth=thiid[4])
#col=local_cmaps.parula(colid[5])
#axes[ai,aj].plot(CanupEOS.hug.P,CanupEOS.hug.S*1.e3,linid[5],color=col,markersize=msize,label=labid[5],linewidth=thiid[5])
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
axes[ai,aj].plot(TmpEOS.vc.Sl*1.E3,TmpEOS.vc.T,linid[labind],color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.vc.Sv*1.E3,TmpEOS.vc.T,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.cp.S*1.E3,TmpEOS.cp.T,'o',color=col)
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.Sl*1.E3,TmpEOS.mc.T,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.mc.Ss*1.E3,TmpEOS.mc.T,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].set_ylim(0,1.5*NewEOS.cp.T)
axes[ai,aj].set_xlim(0,14)
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Temperature [K]',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------------------
# density-pressure
ai=0
aj=1
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
axes[ai,aj].loglog(TmpEOS.vc.rl,TmpEOS.vc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.vc.rv,TmpEOS.vc.Pv,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.cp.rho,TmpEOS.cp.P,'o',color=col)
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.rl,TmpEOS.mc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.mc.rs,TmpEOS.mc.Ps,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].set_ylim(1.e-5,300)
axes[ai,aj].set_xlim(1.e-1,8)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#------
#entropy-pressure
ai=1
aj=0
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
axes[ai,aj].semilogy(TmpEOS.vc.Sl*1.E3,TmpEOS.vc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.vc.Sv*1.E3,TmpEOS.vc.Pv,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.cp.S*1.E3,TmpEOS.cp.P,'o',color=col)
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.Sl*1.E3,TmpEOS.mc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.mc.Ss*1.E3,TmpEOS.mc.Ps,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.hug.S*1.E3,TmpEOS.hug.P,'--',color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.hug.S[0]*1.E3,TmpEOS.hug.P[0],'o',color=col)
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(1.e-10,10000)
axes[ai,aj].set_xlim(0,14)
#-----------
# specific energy - pressure
ai=1
aj=1
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
axes[ai,aj].semilogy(TmpEOS.vc.Ul,TmpEOS.vc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.vc.Uv,TmpEOS.vc.Pv,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.cp.U,TmpEOS.cp.P,'o',color=col)
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.Ul,TmpEOS.mc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.mc.Us,TmpEOS.mc.Ps,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.hug.U,TmpEOS.hug.P,'--',color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.hug.U[0],TmpEOS.hug.P[0],'o',color=col)
axes[ai,aj].set_xlabel('Specific Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(1.e-11,10000)
axes[ai,aj].set_xlim(-3,NewEOS.cp.U*2.)
#-------
# temperature - pressure
ai=2
aj=0
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
axes[ai,aj].semilogy(TmpEOS.vc.T,TmpEOS.vc.Pv,linid[labind],color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.cp.T,TmpEOS.cp.P,'o',color=col)
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.T,TmpEOS.mc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].set_xlabel('Temperature (K)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_xlim(0,9000)
axes[ai,aj].set_ylim(1.e-16,100)
#-------
# pressure - temperature melt curve
ai=2
aj=1
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.Pl,TmpEOS.mc.T,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.hug.P,TmpEOS.hug.T,'--',color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.hug.P[0],TmpEOS.hug.T[0],'o',color=col)
axes[ai,aj].set_ylabel('Temperature (K)',size=sfont)
axes[ai,aj].set_xlabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(0,9000)
axes[ai,aj].set_xlim(-5,450)
axes[ai,aj].annotate('Solid - Melt curves\nDashed - Hugoniots',(10,8000))
#-------
# density - pressure melt curve
ai=3
aj=0
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.rl,TmpEOS.mc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.mc.rs,TmpEOS.mc.Ps,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.hug.rho,TmpEOS.hug.P,'--',color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.hug.rho[0],TmpEOS.hug.P[0],'o',color=col)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(100,350)
axes[ai,aj].set_xlim(4.5,6.5)
axes[ai,aj].annotate('Solid - Melt curves\nDashed - Hugoniots',(5.75,120))
#-------------------------
# density-pressure
ai=3
aj=1
for ii in [3,0,1,2]:
if ii == 0:
labind = 3
TmpEOS = deepcopy(IsaleEOS)
if ii == 1:
labind = 4
TmpEOS = deepcopy(GadgetEOS)
if ii == 2:
labind = 5
TmpEOS = deepcopy(CanupEOS)
if ii == 3:
labind = 0
TmpEOS = deepcopy(NewEOS)
col=local_cmaps.parula(colid[labind])
axes[ai,aj].loglog(TmpEOS.vc.rl,TmpEOS.vc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind],label=labid3[labind])
axes[ai,aj].plot(TmpEOS.vc.rv,TmpEOS.vc.Pv,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.cp.rho,TmpEOS.cp.P,'o',color=col)
if TmpEOS.tp.T > 0:
axes[ai,aj].plot(TmpEOS.mc.rl,TmpEOS.mc.Pl,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].plot(TmpEOS.mc.rs,TmpEOS.mc.Ps,linid[labind],color=col,markersize=msize,linewidth=thiid[labind])
axes[ai,aj].set_ylim(1.e-10,1000)
axes[ai,aj].set_xlim(1.e-10,10)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#===================================================================
# PLOT EXPERIMENTAL CONSTRAINTS ON THE ANEOS PHASE BOUNDARIES
PLOTDATA=1
datms = 8
if PLOTDATA:
# entropy-temperature [0,0]
ai=0
aj=0
#axes[ai,aj].plot(5.149,5130,'^',markersize=datms,color='cyan',label='Qtz Kraus et al. 2012')
# 0.6689 kJ/kg STP entropy from Robie et al. 1982
axes[ai,aj].plot(0.669,298,'+',color='orange',label='STP')
# 1 bar melting point entropy, enthalpy and temperature from Richet et al. 1993
#axes[ai,aj].plot(3.470,2174,'d',color='orange',label='MP 1 bar Richet et al. 1993')
# Triple point from Nagahara et al. 1994
#Triple point of forsterite 5.2e-5 bar, 1890 C (2163 K)
axes[ai,aj].plot(3.470,2163,'X',color='orange',label='TP Nagahara et al. 1994')
# density-pressure [0,1]
ai=0
aj=1
#axes[ai,aj].plot([2.687,2.9468],[1.E-4,1.E-4],'<',markersize=datms,color='orange',label='MELTS MP') # Berman solid, Lange liquid
#axes[ai,aj].plot(0.4822,0.1414,'+',label='En Xiao & Stixrude 2018',markersize=datms,color='brown')
#axes[ai,aj].plot(0.508,0.132,'^',label='Qtz Kraus et al. 2012',markersize=datms,color='cyan')
# entropy -- pressure [1,0]
ai=1
aj=0
# 0.6689 kJ/kg STP entropy from Robie et al. 1982
axes[ai,aj].plot(0.669,1.e-4,'+',color='orange',label='STP')
# 1 bar melting point entropy, enthalpy and temperature from Richet et al. 1993
axes[ai,aj].plot(3.470,1.e-4,'d',color='orange',label='MP 1 bar Richet et al. 1993')
# Triple point from Nagahara et al. 1994
#Triple point of forsterite 5.2e-5 bar, 1890 C (2163 K)
axes[ai,aj].plot(3.470,5.2e-9,'X',color='orange',label='TP Nagahara et al. 1994')
# temperature -- pressure [2,0]
ai=2
aj=0
# Triple point from Nagahara et al. 1994
#Triple point of forsterite 5.2e-5 bar, 1890 C (2163 K)
axes[ai,aj].plot(2163.,5.2e-9,'X',color='orange',label='TP Nagahara et al. 1994')
# Melt curve points
axes[ai,aj].plot(2174,1.e-4,'d',color='orange',label='Richet et al. 1993')
axes[ai,aj].plot(2550,13.,'v',color='orange',label='de Koker et al. 2009')
# Nagahara et al. 1994 vapor curve of forsterite
tvapfo = np.arange(46)*10.+1400.+273. # in C to K
#pvapfo = np.exp(-77955.0/tvapfo+27.7)
pvapfonagahara = np.exp(169.-543.e3/(8.314*(tvapfo)))
#print(pvapfonagahara)
#print(tvapfo)
#print(pvapfo)
#axes[3,0].plot(tvapfo+273.,pvapfo*1.e5/1.e9,linestyle='-',color='orange',label='Sublimation curve\nMysen & Kushiro 1988')
#axes[3,0].plot(tvapfo,pvapfonagahara*1.e5/1.e9,linestyle='-',color='green',label='Sublimation curve\nNagahara et al. 1994')
#print(pvapfonagahara)
tt=np.zeros(7)
tt.fill(273.)
tt=tt+np.asarray([1400.,1500.,1600.,1700.,1725.,1760.,1800.])
axes[ai,aj].plot(tt,np.asarray([8.79E-9,5.98E-8,3.85E-7,2.7E-6,4.21E-6,9.58E-6,1.52E-5])/1.e4,'-x',color='orange',label='Nagahara et al. 1994')
#Centolanzi and Chapman Tektite vapor curve
#tvaptek = np.arange(1400)+1700. # in K
#pvaptek = np.exp(-57400.0/tvaptek+18.5)*101325. # in atm to Pa
#axes[ai,aj].plot(tvaptek,pvaptek/1.e9,linestyle='-',color='cyan',label='Vapor curve tektites\nCentolanzi & Chapman 1966')
# pressure- temperature [2,1]
ai=2
aj=1
# Melt curve points
axes[ai,aj].plot(1.e-4,2174,'d',color='orange',label='Richet et al. 1993')
axes[ai,aj].plot(13.,2550,'v',color='orange',label='de Koker et al. 2009')
# Luo et al. 2004 reanalyzed temperature point
#5.86(15) 4810(70) 188(6)
axes[ai,aj].errorbar([188],[4810],xerr=[6],yerr=[70],fmt='^',color='orange',label='Luo et al. 2004 Olivine')
axes[ai,aj].plot(Mosenfelderdatarr.iloc[:,0].values,Mosenfelderdatarr.iloc[:,1].values,linestyle='-',color='brown',linewidth=1,label='Forsterite Melt Curve\n(Mosenfelder et al. 2007)')
#axes[ai,aj].plot(peridotiteliquidusdatarr.iloc[:,0].values,peridotiteliquidusdatarr.iloc[:,1].values,linestyle='-',color='orange',label='Peridotite Liquidus')
#axes[ai,aj].plot(peridotitesolidusdatarr.iloc[:,0].values,peridotitesolidusdatarr.iloc[:,1].values,linestyle=':',color='orange',label='Peridotite Solidus\n(Fiquet et al. 2010)')
#####OMEGA data from Root et al. 2018
col=local_cmaps.parula(0.5)
axes[ai,aj].fill_between(OM_D1P*1000,(OM_DT1-OM_DTe1),(OM_DT1+OM_DTe1),label="OMEGA data (Root et al. 2018)",
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D2P*1000,(OM_DT2-OM_DTe2),(OM_DT2+OM_DTe2),
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D3P*1000,(OM_DT3-OM_DTe3),(OM_DT3+OM_DTe3),
color=col,alpha=0.25)
axes[ai,aj].fill_between(OM_D4P*1000,(OM_DT4-OM_DTe4),(OM_DT4+OM_DTe4),
color=col,alpha=0.25)
axes[ai,aj].plot(QMDH_p[1::],QMDH_t[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].errorbar(ZTdat_p,ZTdat_t,xerr=ZTdat_perr,yerr=ZTdat_terr/1.E3,fmt=stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3],elinewidth=1)
# density - pressure [3,0]
ai=3
aj=0
# Melt Hugoniot Points from Mosenfelder et al. 2007
axes[ai,aj].errorbar([5.48],[188.5],xerr=[0.6],yerr=[2.0],fmt='o',color='orange',label='Hugoniot "melt point" from\nMosenfelder et al. 2007')
# QMD Root et al. 2018
axes[ai,aj].plot(QMDH_r[1::],QMDH_p[1::],styleqmd[0],markersize=styleqmd[2],color=styleqmd[1],label=styleqmd[3])
axes[ai,aj].errorbar(Zdat_r,Zdat_p,xerr=Zdat_rerr,yerr=Zdat_perr,fmt=stylezdat[0],markersize=stylezdat[2],color=stylezdat[1],label=stylezdat[3])
# Luo et al. 2004 reanalyzed temperature point
#5.86(15) 4810(70) 188(6)
axes[ai,aj].errorbar([5.86],[188],xerr=[0.15],yerr=[6],fmt='^',color='orange',label='Luo et al. 2004 Olivine')
axes[0,0].legend(fontsize=sfont-5)
axes[0,1].legend(fontsize=sfont-5)
axes[1,0].legend(fontsize=sfont-5,loc='upper right')
axes[1,1].legend(fontsize=sfont-5)
axes[2,0].legend(fontsize=sfont-5)
axes[2,1].legend(fontsize=sfont-5)
axes[3,0].legend(fontsize=sfont-5)
axes[3,1].legend(fontsize=sfont-5)
plt.tight_layout(pad=0.6)
plt.savefig('Stewart-etal-2019-compare-aneos-boundaries.pdf', format='pdf', dpi=1000,transparent=True)
#--------
Check the grid spacing compared to the phase boundaries¶
Colors correspond to temperature. Black lines are ANEOS phase boundaries.
Note that ANEOS by default puts a tension region in for the solid that extends to rhomin (V17) in the input file.
If the tension region is kept, it is visible as a kink connects to the low entropy extension of the melt curve in the lower left plot of density vs. specific entropy.
The lack of points below 1000 K in the vapor dome (seen in temperature vs. specific entropy upper left) corresponds to when the sublimation pressure reaches 1.E-30. At this point, ANEOS bottoms out the pressures at this value and fixes the other state variables (it looks like to constant values; will investigate this region more closely later).
The ANEOS triple point convergence is not perfect, and there are kinks in the tabulated phase boundaries right at the triple point.
In [27]:
# check the gridding of the table around the vapor curve
# Plot aneos vapor curves
sfont = 15
fig, axes = plt.subplots(nrows=5, ncols=2, figsize=(14,26))
plt.subplots_adjust(wspace=0.4)
tcolmin=0.
tcolmax=1.2*NewEOS.cp.T
tpltmax=1.2*NewEOS.cp.T
tskip=1
#-------------
ai=0
aj=0
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Temperature [K]',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
axes[ai,aj].set_ylim(0,tpltmax)
axes[ai,aj].set_xlim(0,25)
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.S[it,:]*1.e3,np.zeros(NewEOS.ND)+NewEOS.T[it],'o',markersize=2,color=col)
axes[ai,aj].plot(NewEOS.vc.Sl*1.e3,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.vc.Sv*1.e3,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.cp.S*1.e3,NewEOS.cp.T,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Sl*1.e3,NewEOS.mc.T,color="black")
axes[ai,aj].plot(NewEOS.mc.Ss*1.e3,NewEOS.mc.T,color="black")
#-------------
ai=0
aj=1
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.P[it,:],'o',markersize=2,color=col)
axes[ai,aj].loglog(NewEOS.vc.rl,NewEOS.vc.Pl,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.Pv,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.P,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(1.e-25,1000)
axes[ai,aj].set_xlim(1.e-20,10.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=1
aj=0
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.S[it,:]*1.E3,NewEOS.P[it,:],'o',markersize=2,color=col)
axes[ai,aj].semilogy(NewEOS.vc.Sl*1.e3,NewEOS.vc.Pl,color="black")
axes[ai,aj].plot(NewEOS.vc.Sv*1.e3,NewEOS.vc.Pv,color="black")
axes[ai,aj].plot(NewEOS.cp.S*1.e3,NewEOS.cp.P,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Sl*1.e3,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.Ss*1.e3,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(1.e-10,1000)
axes[ai,aj].set_xlim(0,15)
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=1
aj=1
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.U[it,:],NewEOS.P[it,:],'o',markersize=2,color=col)
axes[ai,aj].semilogy(NewEOS.vc.Ul,NewEOS.vc.Pl,color="black")
axes[ai,aj].plot(NewEOS.vc.Uv,NewEOS.vc.Pv,color="black")
axes[ai,aj].plot(NewEOS.cp.U,NewEOS.cp.P,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Ul,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.Us,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(1.e-10,1000)
axes[ai,aj].set_xlim(0,25)
axes[ai,aj].set_xlabel('Specific Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=2
aj=0
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,np.zeros(NewEOS.ND)+NewEOS.T[it],'o',markersize=2,color=col)
axes[ai,aj].plot(NewEOS.vc.rl,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.T,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.T,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.T,color="black")
axes[ai,aj].set_ylim(0.,20000)
axes[ai,aj].set_xlim(0,30.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Temperature (K)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=2
aj=1
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].loglog(NewEOS.rho,np.zeros(NewEOS.ND)+NewEOS.T[it],'o',markersize=2,color=col)
axes[ai,aj].semilogx(NewEOS.vc.rl,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.T,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.T,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.T,color="black")
axes[ai,aj].set_ylim(10.,1.E8)
axes[ai,aj].set_xlim(1.E-10,100.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Temperature (K)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=3
aj=0
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.S[it,:]*1000.,'o',markersize=2,color=col)
axes[ai,aj].plot(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.S*1.E3,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ss*1.E3,color="black")
axes[ai,aj].set_ylim(0.,10)
axes[ai,aj].set_xlim(0.,15.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=3
aj=1
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].semilogx(NewEOS.rho,NewEOS.S[it,:]*1000.,'o',markersize=2,color=col)
axes[ai,aj].semilogx(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.S*1.E3,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ss*1.E3,color="black")
axes[ai,aj].set_ylim(0.,20)
axes[ai,aj].set_xlim(1.E-15,30.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=4
aj=1
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].semilogx(NewEOS.rho,NewEOS.S[it,:]*1000.,'o',markersize=2,color=col)
axes[ai,aj].semilogx(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.S*1.E3,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ss*1.E3,color="black")
axes[ai,aj].set_ylim(0.,30)
axes[ai,aj].set_xlim(1.E-25,30.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=4
aj=0
tcolmax=40000.
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].semilogx(NewEOS.rho,NewEOS.S[it,:]*1000.,'o',markersize=2,color=col)
axes[ai,aj].semilogx(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.S*1.E3,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ss*1.E3,color="black")
axes[ai,aj].set_ylim(0.,200)
axes[ai,aj].set_xlim(1.E-25,30.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#axes[0,0].legend(fontsize=sfont-5)
#axes[0,1].legend(fontsize=sfont-5)
#axes[1,0].legend(fontsize=sfont-5)
#axes[1,1].legend(fontsize=sfont-5)
ANEOS KPA FLAG¶
TABLE ANEOS
KPAQQ=STATE INDICATOR =1, 1p =1, 1p (eos without melt)
=2, 2p lv =2, 2p liquid/solid plus vapor
=4, 1p solid (eos with melt)
=5, 2p melt (eos with melt)
=6, 1p liquid (eos with melt)
=-1 bad value of temperature
=-2 bad value of density
=-3 bad value of material number
To resolve a melt curve, there should be sufficient numbers of points within the melt curve (KPA=5, red points) so that the melt curve is continuously sampled in the grid.
The pink region is where the vapor pressure is bottomed out at 1.E-30 GPa or the pressures are negative (if there is a tension region.)
Every 10th isotherm is plotted.
In [28]:
# check the ANEOS quality flag for errors in the EOS surface
uniqkarr = np.unique(NewEOS.KPA)
print("Unique values in the KPA flag array:", uniqkarr)
print("Value: # elements with this value")
#get_indexes = lambda x, xs: [i for (y, i) in zip(xs, range(len(xs))) if x == y]
for i in uniqkarr:
ix = get_indexes(i,np.reshape(NewEOS.KPA,NewEOS.ND*NewEOS.NT))
print(i,': ',len(ix))
# Plot aneos vapor curves
sfont = 15
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14,14))
plt.subplots_adjust(wspace=0.4)
kcolmin=1
kcolmax=7
tskip=10
#-------------
#-------------
ai=0
aj=0
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Temperature (K)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for itt in range(1,NewEOS.NT,tskip):
for i in uniqkarr:
ix = get_indexes(i,NewEOS.KPA[itt,:])
icolscale = (i-kcolmin)/(kcolmax-kcolmin)
col=local_cmaps.parula(icolscale)
if i == 5:
axes[ai,aj].plot(NewEOS.rho[ix],np.full(len(ix),NewEOS.T[itt]),'o',markersize=5,color='red')
# print(i,andarr[ix],antarr[itt])
else:
axes[ai,aj].plot(NewEOS.rho[ix],np.full(len(ix),NewEOS.T[itt]),'o',markersize=2,color=col)
axes[ai,aj].plot(NewEOS.vc.rl,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.T,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.T,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.T,color="black")
axes[ai,aj].set_ylim(0.,20000)
axes[ai,aj].set_xlim(0,30.)
#-------------
ai=0
aj=1
for itt in range(1,NewEOS.NT,tskip):
for i in uniqkarr:
ix = get_indexes(i,NewEOS.KPA[itt,:])
icolscale = (i-kcolmin)/(kcolmax-kcolmin)
col=local_cmaps.parula(icolscale)
if i == 5:
axes[ai,aj].loglog(NewEOS.rho[ix],np.full(len(ix),NewEOS.T[itt]),'o',markersize=5,color='red')
# print(i,andarr[ix],antarr[itt])
else:
axes[ai,aj].loglog(NewEOS.rho[ix],np.full(len(ix),NewEOS.T[itt]),'o',markersize=2,color=col)
axes[ai,aj].loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.T,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.T,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.T,color="black")
axes[ai,aj].set_ylim(10.,1.E8)
axes[ai,aj].set_xlim(1.E-22,100.)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Temperature (K)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=1
aj=0
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for itt in range(1,NewEOS.NT,tskip):
for i in uniqkarr:
ix = get_indexes(i,NewEOS.KPA[itt,:])
icolscale = (i-kcolmin)/(kcolmax-kcolmin)
col=local_cmaps.parula(icolscale)
if i == 5:
axes[ai,aj].semilogy(NewEOS.rho[ix],NewEOS.P[itt,ix],'o',markersize=5,color='red')
# print(i,andarr[ix],antarr[itt])
else:
axes[ai,aj].semilogy(NewEOS.rho[ix],NewEOS.P[itt,ix],'o',markersize=2,color=col)
axes[ai,aj].semilogy(NewEOS.vc.rl,NewEOS.vc.Pl,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.Pv,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.P,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(1.e-6,2000)
axes[ai,aj].set_xlim(0,13.)
#-------------
ai=1
aj=1
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Temperature (K)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for itt in range(1,NewEOS.NT,tskip):
for i in uniqkarr:
ix = get_indexes(i,NewEOS.KPA[itt,:])
icolscale = (i-kcolmin)/(kcolmax-kcolmin)
col=local_cmaps.parula(icolscale)
if i == 5:
axes[ai,aj].plot(NewEOS.rho[ix],np.full(len(ix),NewEOS.T[itt]),'o',markersize=5,color='red')
# print(i,andarr[ix],antarr[itt])
else:
axes[ai,aj].plot(NewEOS.rho[ix],np.full(len(ix),NewEOS.T[itt]),'o',markersize=2,color=col)
tmp = np.where(NewEOS.P[itt,:] < 0.)
if (len(tmp[0]) > 0):
axes[ai,aj].plot(NewEOS.rho[tmp[0]],np.full(len(tmp[0]),NewEOS.T[itt]),'o',markersize=2,color='purple')
tmp = np.where(NewEOS.P[itt,:]*1.e30 <= 2.)
if (len(tmp[0]) > 0):
axes[ai,aj].plot(NewEOS.rho[tmp[0]],np.full(len(tmp[0]),NewEOS.T[itt]),'o',markersize=2,color='hotpink')
axes[ai,aj].loglog(NewEOS.vc.rl,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.vc.rv,NewEOS.vc.T,color="black")
axes[ai,aj].plot(NewEOS.cp.rho,NewEOS.cp.T,'o',color="black")
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.T,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.T,color="black")
axes[ai,aj].set_ylim(10.,1.E8)
axes[ai,aj].set_xlim(1.E-22,100.)
fig.show()
Check the Melt Curve in Tabulated EOS¶
Colored lines correspond to isotherms. Black lines are ANEOS phase boundaries.
Tabulations of the equation of state can lead to erroneous material descriptions across the melt curve. In the following plots, the isotherms should be flat (constant pressure) across the phase boundary (black lines). Every 10th isotherm in the table is shown in the plotted regions.
In [29]:
# CHECK MELT CURVE GRIDDING
sfont = 15
fig, axes = plt.subplots(nrows=5, ncols=2, figsize=(14,26))
plt.subplots_adjust(wspace=0.5)
tcolmin=0.
tcolmax=1.5*NewEOS.cp.T
tpltmax=1.5*NewEOS.cp.T
tskip=10
#-------------
ai=0
aj=0
axes[ai,aj].plot([],[],' ',label='Low pressure melt curve')
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(.1,60)
axes[ai,aj].set_xlim(2.4,4.5)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=0
aj=1
axes[ai,aj].plot([],[],' ',label='High pressure melt curve')
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(40.,150)
axes[ai,aj].set_xlim(3.9,5.4)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=1
aj=0
axes[ai,aj].plot([],[],' ',label='Higher pressure melt curve')
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(180.,310)
axes[ai,aj].set_xlim(5.5,6.4)
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=1
aj=1
axes[ai,aj].plot([],[],' ',label='Higher pressure melt curve')
axes[ai,aj].set_xlabel('Specific Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.U[it,:],NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Ul,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.Us,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(180.,310)
axes[ai,aj].set_xlim(7,20)
#-------------
ai=2
aj=0
axes[ai,aj].plot([],[],' ',label='Low pressure melt curve')
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.S[it,:]*1.e3,NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Sl*1.e3,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.Ss*1.e3,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(.1,50)
axes[ai,aj].set_xlim(2.6,4.)
#-------------
ai=2
aj=1
axes[ai,aj].plot([],[],' ',label='High pressure melt curve')
axes[ai,aj].set_xlabel('Specific Entropy (kJ/K/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.S[it,:]*1.e3,NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Sl*1.e3,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.Ss*1.e3,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(50.,150)
axes[ai,aj].set_xlim(2.6,4.2)
#-------------
ai=3
aj=0
axes[ai,aj].plot([],[],' ',label='Low pressure melt curve')
axes[ai,aj].set_xlabel('Specific Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.U[it,:],NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Ul,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.Us,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_xlim(1,7)
axes[ai,aj].set_ylim(.1,50)
#-------------
ai=3
aj=1
axes[ai,aj].plot([],[],' ',label='High pressure melt curve')
axes[ai,aj].set_xlabel('Specific Energy (MJ/kg)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.U[it,:],NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.Ul,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.Us,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(50.,150)
axes[ai,aj].set_xlim(1,15)
#-------------
ai=4
aj=0
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.P[it,:],'o',markersize=2,color=col,linestyle='-')
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(300,700)
axes[ai,aj].set_xlim(6.5,8.)
axes[ai,aj].plot([],[],' ',label='Very high pressure melt curve.')
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#-------------
ai=4
aj=1
for it in range(1,NewEOS.NT,tskip):
icolscale = (NewEOS.T[it]-tcolmin)/(tcolmax-tcolmin)
col=local_cmaps.parula(icolscale)
axes[ai,aj].plot(NewEOS.rho,NewEOS.P[it,:],'o',markersize=2,linestyle='-',color=col)
if NewEOS.tp.T > 0:
axes[ai,aj].plot(NewEOS.mc.rl,NewEOS.mc.Pl,color="black")
axes[ai,aj].plot(NewEOS.mc.rs,NewEOS.mc.Ps,color="black")
axes[ai,aj].set_ylim(700,1200)
axes[ai,aj].set_xlim(8.25,9.5)
axes[ai,aj].plot([],[],' ',label='Very high pressures')
axes[ai,aj].set_xlabel('Density (g/cm$^3$)',size=sfont)
axes[ai,aj].set_ylabel('Pressure (GPa)',size=sfont)
axes[ai,aj].tick_params(labelsize=sfont)
#------
axes[0,0].legend(fontsize=sfont-5)
axes[0,1].legend(fontsize=sfont-5)
axes[1,0].legend(fontsize=sfont-5)
axes[1,1].legend(fontsize=sfont-5)
axes[2,0].legend(fontsize=sfont-5)
axes[2,1].legend(fontsize=sfont-5)
axes[3,0].legend(fontsize=sfont-5)
axes[3,1].legend(fontsize=sfont-5)
axes[4,0].legend(fontsize=sfont-5)
axes[4,1].legend(fontsize=sfont-5)
Out[29]:
Example of bad gridding across the melt curve¶
The isotherms should be flat across the phase boundary, but the poor gridding leads to varying errors along the phase boundary. These errors would lead to energy errors and non-conservative behavior in the EOS model.
PLOT GADGET2 FORMAT TABLE: Entropy-Density grid¶
Color contour plots of the GADGET Rho-S table¶
The SESAME table and GADGET table use the same density array. So the GADGET table is linearly interpolated along a density-column to find the new table values at each point in the GADGET entropy grid.
Errors in the interpolation, particularly near phase boundaries, can be seen in the sound speeds and KPA flags.
In [30]:
if MAKEGADGETTABLE == 1:
# PLOT COLOR SHADED VALUES RHO-S TABLE
lw=1
sfont = 15
ds = (10,10)
fig, ([ax0, ax1], [ax2,ax3], [ax4,ax5])= plt.subplots(nrows=3,ncols=2,figsize=(14,22))
plt.subplots_adjust(wspace=0.4)
##================ Pressure
im1=ax0.pcolormesh(GadEOS.rho,GadEOS.S*1.e3,(np.log10(GadEOS.P)+25)/29.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax0.plot(NewEOS.vc.rl,NewEOS.vc.Sl*1.e3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.e3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.e3,'ko')
if NewEOS.mc.NT > 0:
ax0.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax0.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.set_ylim(0.,15)
ax0.set_xlim(0,30.)
ax0.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax0.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax0.set_title('Colors=log$_{10}$(P (GPa))',size=sfont)
ax0.tick_params(labelsize=sfont)
divider0 = make_axes_locatable(ax0)
cax0 = divider0.append_axes('right', size='5%', pad=0.05)
cbar0 = fig.colorbar(im1, cax=cax0, ticks = [],orientation='vertical')
#cbar0.ax.set_yticklabels([' ',' ',' ']) # vertical colorbar
cbar0.set_label('Log$_{10}$(P) [GPa]',size=sfont)
#cbar0.ax.set_yticklabels(['-25','-11','+4']) # vertical colorbar
im1=ax1.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(np.log10(GadEOS.P)+25)/29.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax1.loglog(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.plot(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax1.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax1.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.set_ylim(0.1,300)
ax1.set_xlim(1.E-21,100.)
ax1.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax1.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax1.set_title('Colors=log$_{10}$(P (GPa))',size=sfont)
ax1.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax1)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-25','-11', '+4']) # vertical colorbar
cbar.set_label('Log$_{10}$(P) [GPa]',size=sfont)
#================ Sp. Int. Energy
im1=ax2.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(np.log10(GadEOS.U)+4.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax2.plot(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax2.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax2.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.set_ylim(0.,15)
ax2.set_xlim(0,30.)
ax2.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax2.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax2.set_title('Colors=log$_{10}$(Sp. Int. Energy (MJ/kg))',size=sfont)
ax2.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax2)
cax = divider.append_axes('right', size='5%', pad=0.05)
# does not want to label ticks in this location
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['-4','+1','+6']) # vertical colorbar
cbar.set_label('Log$_{10}$(E) [MJ/kg]',size=sfont)
ax3.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(np.log10(GadEOS.U)+4.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax3.loglog(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax3.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax3.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.set_ylim(.1,300)
ax3.set_xlim(1.E-21,100.)
ax3.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax3.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax3.set_title('Colors=log$_{10}$(E (MJ/kg))',size=sfont)
ax3.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax3)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-4', '+1','+6']) # vertical colorbar
cbar.set_label('Log$_{10}$(E) [MJ/kg]',size=sfont)
#================ Temperature
im1=ax4.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(np.log10(GadEOS.T)-2)/4.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax4.plot(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax4.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax4.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.set_ylim(0.,15)
ax4.set_xlim(0,30.)
ax4.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax4.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax4.set_title('Colors=log$_{10}$(Temperature (K))',size=sfont)
ax4.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax4)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['2', '4', '6']) # vertical colorbar
cbar.set_label('Log$_{10}$(T) [K]',size=sfont)
ax5.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(np.log10(GadEOS.T)-2)/4.,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax5.loglog(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax5.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax5.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.set_ylim(.1,300)
ax5.set_xlim(1.E-21,100.)
ax5.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax5.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax5.set_title('Colors=log$_{10}$(Temperature (K))',size=sfont)
ax5.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax5)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['2', '4','6']) # vertical colorbar
cbar.set_label('Log$_{10}$(T) [K]',size=sfont)
plt.show()
##============= start new plot
fig2, ([ax0, ax1], [ax2,ax3], [ax4,ax5])= plt.subplots(nrows=3,ncols=2,figsize=(14,22))
plt.subplots_adjust(wspace=0.4)
#================ Sound Speed
im1=ax0.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(np.log10(GadEOS.cs)+3.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax0.plot(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.plot(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax0.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax0.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax0.set_ylim(0.,15)
ax0.set_xlim(0,30.)
ax0.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax0.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax0.set_title('Colors=log$_{10}$(Sound Speed (cm/s))',size=sfont)
ax0.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax0)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['-3', '+2', '+7']) # vertical colorbar
cbar.set_label('Log$_{10}$(cs) [cm/s]',size=sfont)
ax1.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(np.log10(GadEOS.cs)+3.)/10.,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax1.loglog(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.loglog(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.loglog(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax1.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax1.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax1.set_ylim(.1,300)
ax1.set_xlim(1.E-21,100.)
ax1.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax1.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax1.set_title('Colors=log$_{10}$(sound speed (cm/s))',size=sfont)
ax1.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax1)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-3', '+2', '+7']) # vertical colorbar
cbar.set_label('Log$_{10}$(cs) [cm/s]',size=sfont)
#================ HFE
amin = np.min(GadEOS.A)
amin = -1000.
alogmax = 1500. #np.max(anaarrodd)-amin #np.max(np.log10(anaarrodd-amin))
#print('amin, log10(amin)',amin,np.log10(-amin))
#print('alogmax=',alogmax)
im1=ax2.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(GadEOS.A-amin)/alogmax,cmap=local_cmaps.parula,vmin=0,vmax=1,edgecolors='face')
ax2.plot(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.plot(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax2.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax2.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax2.set_ylim(0.,15)
ax2.set_xlim(0,30.)
ax2.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax2.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax2.set_title('Colors=HFE (MJ/kg)',size=sfont)
ax2.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax2)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['-1000','-500','0','500']) # vertical colorbar
cbar.set_label('Log$_{10}$(HFE) [MJ/kg]',size=sfont)
ax3.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,(GadEOS.A-amin)/alogmax,cmap=local_cmaps.parula,vmin=0,vmax=1)
ax3.loglog(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.loglog(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax3.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax3.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax3.set_ylim(.1,300)
ax3.set_xlim(1.E-21,100.)
ax3.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax3.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax3.set_title('Colors=HFE (MJ/kg)',size=sfont)
ax3.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax3)
cax = divider.append_axes('right', size='5%', pad=0.05)
#cbar = fig.colorbar(im1, cax=cax, ticks = [0, 0.5, 1], orientation='vertical')
#cbar.ax.set_yticklabels(['-6', '-3.5', '-1']) # vertical colorbar
cbar = fig.colorbar(im1, cax=cax, ticks = [0,.333,.6667, 1], orientation='vertical')
cbar.ax.set_yticklabels(['-1000','-500','0','500']) # vertical colorbar
cbar.set_label('Log$_{10}$(HFE) [MJ/kg]',size=sfont)
#================ KPA flag
cmap2 = cm.get_cmap('plasma', 6) # 6 discrete colors
im1=ax4.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,((GadEOS.KPA)-0.5)/6.,cmap=cmap2,vmin=0,vmax=1,edgecolors='face')
ax4.plot(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax4.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.plot(NewEOS.mc.rs,NewEOS.mc.Ss*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax4.set_ylim(0.,15)
ax4.set_xlim(0,30.)
ax4.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax4.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax4.set_title('Colors=KPA flag',size=sfont)
ax4.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax4)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = [], orientation='vertical')
#cbar.ax.set_yticklabels(['0','1','2','3','4','5', '6']) # vertical colorbar
cbar.set_label('KPA flag',size=sfont)
ax5.pcolormesh(GadEOS.rho,GadEOS.S*1.E3,((GadEOS.KPA)-0.5)/6.,cmap=cmap2,vmin=0,vmax=1)
ax5.loglog(NewEOS.vc.rl,NewEOS.vc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rv,NewEOS.vc.Sv*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.loglog(NewEOS.vc.rl[0],NewEOS.vc.Sl[0]*1.E3,'ko')
if NewEOS.mc.NT > 0:
ax5.plot(NewEOS.mc.rl,NewEOS.mc.Sl*1.E3,color="black",linewidth=lw,linestyle='--',dashes=ds)
# ax5.plot(NewEOS.mc.rs,NewEOS.mc.T,color="black",linewidth=lw,linestyle='--',dashes=ds)
ax5.set_ylim(.1,300)
ax5.set_xlim(1.E-21,100.)
ax5.set_xlabel('Density (g/cm$^3$)',size=sfont)
ax5.set_ylabel('Specific Entropy (kJ/K/kg)',size=sfont)
ax5.set_title('Colors=KPA flag',size=sfont)
ax5.tick_params(labelsize=sfont)
divider = make_axes_locatable(ax5)
cax = divider.append_axes('right', size='5%', pad=0.05)
cbar = fig.colorbar(im1, cax=cax, ticks = np.arange(13)/12, orientation='vertical')
cbar.ax.set_yticklabels(['','1','','2','','3','','4','','5','', '6']) # vertical colorbar
cbar.set_label('KPA flag',size=sfont)
plt.show()
else:
print("No GADGET2 TABLE requested.")
INTERPOLATION ISSUES¶
The IEP is calculated on the density-temperature grid using the following method:
- Start with a grid that is twice as dense as the desired final grid and generate an ANEOS density-temperature table.
- Split the table into two tables made from the even rows and columns and the odd rows and columns.
- Interpolate for the odd index grid values using the even index table.
- The IEP is given by (interpolated value-original value)/(original value) of the odd index table.
These are the calculated IEP values for this gridded table release using bilinear interpolation. These values are saved in a standard 201-301 table format in file NEW-SESAME.IEPTXT
IEP for Pressure¶
IEP for Specific Internal Energy¶
IEP for Specific Entropy¶
IEP for sound speed¶
IEP for the Helmholtz Free Energy¶
References¶
Andrault, D., Bolfan-Casanova, N., Bouhifd, M. A., Boujibar, A., Garbarino, G., Manthilake, G., ... & Pesce, G. (2017). Toward a coherent model for the melting behavior of the deep Earth’s mantle. Physics of the Earth and Planetary Interiors, 265, 67-81.
Asimow PD, Ghiorso MS (1998) Algorithmic Modifications Extending MELTS to Calculate Subsolidus Phase Relations. American Mineralogist 83, 1127-1131.
Centolanzi, F. J., & Chapman, D. R. (1966). Vapor pressure of tektite glass and its bearing on tektite trajectories determined from aerodynamic analysis. Journal of Geophysical Research, 71(6), 1735-1749.
Chase Jr, M. W., Curnutt, J. L., Downey Jr, J. R., McDonald, R. A., Syverud, A. N., & Valenzuela, E. A. (1982). JANAF thermochemical tables, 1982 supplement. Journal of Physical and Chemical Reference Data, 11(3), 695-940. https://janaf.nist.gov
Costa, G. C., Jacobson, N. S., & Fegley Jr, B. (2017). Vaporization and thermodynamics of forsterite-rich olivine and some implications for silicate atmospheres of hot rocky exoplanets. Icarus, 289, 42-55.
de Koker, N. P., Stixrude, L., & Karki, B. B. (2008). Thermodynamics, structure, dynamics, and freezing of Mg2SiO4 liquid at high pressure. Geochimica et Cosmochimica Acta, 72(5), 1427-1441.
Davies, E.J., Carter, P.J., Root, S., Kraus, R.G., Spaulding, D.K., Stewart, S.T., Jacobsen, S.B. (2019) Silicate Melting and Vaporization during Rocky Planet Formation, J. Geophys. Res. Planets, submitted.
Duffy, T., Madhusudhan, N., & Lee, K. K. M. (2015). 2.07 Mineralogy of Super-Earth Planets. Treatise on Geophysics, Second Edition, Elsevier, Oxford.Duffy, T., Madhusudhan, N., & Lee, K. K. M. (2015). 2.07 Mineralogy of Super-Earth Planets. Treatise on Geophysics, Second Edition, Elsevier, Oxford.
Fiquet, G., Auzende, A. L., Siebert, J., Corgne, A., Bureau, H., Ozawa, H., & Garbarino, G. (2010). Melting of peridotite to 140 gigapascals. Science, 329(5998), 1516-1518.
Gillet, P., Richet, P., Guyot, F., & Fiquet, G. (1991). High‐temperature thermodynamic properties of forsterite. Journal of Geophysical Research: Solid Earth, 96(B7), 11805-11816.
Ghiorso, Mark S., and Sack, Richard O. (1995) Chemical Mass Transfer in Magmatic Processes. IV. A Revised and Internally Consistent Thermodynamic Model for the Interpolation and Extrapolation of Liquid-Solid Equilibria in Magmatic Systems at Elevated Temperatures and Pressures. Contributions to Mineralogy and Petrology, 119, 197-212.
Hosono, N., Karato, S. I., Makino, J., & Saitoh, T. R. (2019). Terrestrial magma ocean origin of the Moon. Nature Geoscience, 1, 418-423.
Jacobsen, S.D., Holl, C.M., Adams, K.A., Fischer, R.A., Martin, E.S., Bina, C.R., Lin, J.F., Prakapenka, V.B., Kubo, A. and Dera, P., 2008. Compression of single-crystal magnesium oxide to 118 GPa and a ruby pressure gauge for helium pressure media. American Mineralogist, 93(11-12), pp.1823-1828.
Kraus, R.G., Stewart, S.T., Swift, D.C., Bolme, C.A., Smith, R.F., Hamel, S., Hammel, B.D., Spaulding, D.K., Hicks, D.G., Eggert, J.H. and Collins, G.W. (2012). Shock vaporization of silica and the thermodynamics of planetary impact events. Journal of Geophysical Research: Planets, 117(E9), E09009, doi:10.1029/2012JE004082.
Kumazawa, M., & Anderson, O. L. (1969). Elastic moduli, pressure derivatives, and temperature derivatives of single‐crystal olivine and single‐crystal forsterite. Journal of Geophysical Research, 74(25), 5961-5972.
Luo, S. N., Akins, J. A., Ahrens, T. J., & Asimow, P. D. (2004). Shock‐compressed MgSiO$_3$ glass, enstatite, olivine, and quartz: Optical emission, temperatures, and melting. Journal of Geophysical Research: Solid Earth, 109(B5).
Lyon, S. P., & Johnson, J. D. (1992). SESAME: The LANL equation of state database. Los Alamos National Laboratories Report LAUR-92-3407, Los Alamos, NM.
Marinova, M. M., Aharonson, O., & Asphaug, E. (2011). Geophysical consequences of planetary-scale impacts into a Mars-like planet. Icarus, 211(2), 960-985.
Mosenfelder, J. L., Asimow, P. D., & Ahrens, T. J. (2007). Thermodynamic properties of Mg2SiO4 liquid at ultra‐high pressures from shock measurements to 200 GPa on forsterite and wadsleyite. Journal of Geophysical Research: Solid Earth, 112(B6).
Mysen, B. O., & Kushiro, I. (1988). Condensation, evaporation, melting, and crystallization in the primitive solar nebula; experimental data in the system MgO-SiO$_2$-H$_2$ to $1.0\times10^{-9}$ bar and 1870 degrees C with variable oxygen fugacity. American Mineralogist, 73(1-2), 1-19.
Nagahara, H., Kushiro, I., & Mysen, B. O. (1994). Evaporation of olivine: Low pressure phase relations of the olivine system and its implication for the origin of chondritic components in the solar nebula. Geochimica et cosmochimica acta, 58(8), 1951-1963.
Richet, P., Leclerc, F., & Benoist, L. (1993). Melting of forsterite and spinel, with implications for the glass transition of Mg$_2$SiO$_4$ liquid. Geophysical Research Letters, 20(16), 1675-1678.
Robie, R. A., Hemingway, B. S., & Takei, H. (1982). Heat capacities and entropies of Mg$_2$SiO$_4$, Mn$_2$SiO$_4$, and Co$_2$SiO$_4$ between 5 and 380 K. American Mineralogist, 67(5-6), 470-482.
Root, S., Townsend, J.P., Davies, E., Lemke, R.W., Bliss, D.E., Fratanduono, D.E., Kraus, R.G., Millot, M., Spaulding, D.K., Shulenburger, L. and Stewart, S.T. (2018). The principal Hugoniot of forsterite to 950 GPa. Geophysical Research Letters, 45(9), 3865-3872.
Thomas, C. W., & Asimow, P. D. (2013). Direct shock compression experiments on premolten forsterite and progress toward a consistent high‐pressure equation of state for CaO‐MgO‐Al$_2$O$_3$‐SiO$_2$‐FeO liquids. Journal of Geophysical Research: Solid Earth, 118(11), 5738-5752.
Tillotson, J. H. (1962). Metallic equations of state for hypervelocity impact (No. GA-3216). General Atomics Division, General Dynamics, San Diego, CA.
Vanpeteghem, C. B., Zhao, J., Angel, R. J., Ross, N. L., & Bolfan‐Casanova, N. (2006). Crystal structure and equation of state of MgSiO3 perovskite. Geophysical Research Letters, 33(3), 2005GL024955.
Xiao, B., & Stixrude, L. (2018). Critical vaporization of MgSiO$_3$. Proceedings of the National Academy of Sciences, 115(21), 5371-5376.
Zeman, M., Holec, M., & Váchal, P. (2019). HerEOS: A framework for consistent treatment of the Equation of State in ALE hydrodynamics. Computers & Mathematics with Applications, 78(2), 483-503.
ANEOS references¶
Collins, Gareth S., and H. Jay Melosh (2014). Improvements to ANEOS for multiple phase transitions. 45th Lunar Planet. Sci. Conf. Abs. 2664.
Melosh, H. J. (2007). A hydrocode equation of state for SiO$_2$. Meteoritics & Planetary Science, 42(12), 2079-2098.
Thompson, S. L. (1990). ANEOS analytic equations of state for shock physics codes input manual. SANDIA REPORT SAND, 89-2951.
Thompson, S. L., & Lauson, H. S. (1974). Improvements in the Chart D radiation-hydrodynamic CODE III: Revised analytic equations of state (No. SC-RR--71-0714). Sandia Labs.
Stewart, S. T. (2019). ANEOS Code Modification: Thermal model adjustment parameter. https://github.com/ststewart/aneos-forsterite-2019/EOS-docs/
ANEOS Input Parameters¶
EOS -1: low temperature solid model
THUG, RHUG: initial state for the Hugoniot calculated in ANEOS.OUTPUT
V01 nelem = 3: 3 elements
V02 model type=4: solid-liquid-gas model with ionization
V03 rho0=3.22 g/cm3: reference state is STP.
V04 T0=298 K: reference state is STP.
V05 P0=1.e6 dynes/cm2: reference state STP.
V06 B0=1.10E12 dynes/cm2: bulk modulus is a compromise value to span the low and high pressure liquid region. The true value for forsterite at STP is 128 GPa (Kumazawa and Anderson 1969).
V07 gamma0=0.65: fitted gamma0 to fit liquid region
V08 Tdebye=-1300.0 K: fitted to match entropy of melting. Negative means use full Debye model. True value for forsterite solid is 768K.
V09 TG model=-1: Slater theory. The overall EOS topology is not sensitive to this model choice.
V10 3*C24=7.5: Fitted value for gamma function to fit the liquid pressure-temperature liquid
V11 Esep=1.70E11 erg/g: Zero temperature separation energy. Fitted to match the triple point pressure.
V12 Tmelt=2163 K: Melting temperature at reference pressure.
V13 C53=0 erg/g: Critical point adjustment parameter. Not used.
V14 C54=0. [dimless]: Critical point adjustment parameter. Not used.
V15 H0=0: Thermal conduction parameter. Not used.
V16 C41=0: Thermal conduction parameter. Not used.
V17 rhomin=2.5 g/cm3: minimum density for the solid. Defines the tension region in the model. The default value is 0.8*rho0 when rhomin=0.
V18=0.0 g/cm3: Solid-solid phase transition parameter. Density at onset of transition. Not used.
V19=0.0 g/cm3: Solid-solid phase transition parameter. Density at end of transition. Not used.
V20=0.0 dynes/cm2: Solid-solid phase transition parameter. Pctr, pressure at the center of the transition. Not used.
V21=0.0: Solid-solid phase transition parameter. First derivative of Pctr with respect to density. Not used.
V22=0.0: Solid-solid phase transition parameter. Second derivative of Pctr with respect to density. Not used.
V23 Hfusion=1.0E10 erg/g: Latent heat of fusion at the reference pressure from lab measurements in Richet et al. 1993.
V24 rhol/rhos=0.935: Volume change on melting. Tweaked to match slope of the melt curve. True value 0.9053 based on MELTS model for forsterite at 1 bar.
V25 upper=0.0: Upper limit to cold compression curve extension. Default=1. Setting to zero means use default value.
V26 lower=0.: Default=0.
V27 alpha=0.3: Liquid model parameter ($0<\alpha<1$, default=0.3).
V28 beta=0.1: Liquid model parameter ($0<\beta<1$, default=0.1). beta cannot be equal to gamma.
V29 gamma=0.3: Liquid model parameter ($0<\gamma<1$, default=0.2). beta cannot be equal to gamma.
V30 C60=0: Gamma model adjustment parameter. Default=0.
V31 C61=-0.82: Gamma model adjustment parameter. Default=0.
V32 C62=0.5: Critical point adjustment parameter. Default=0. ($0<C63<1$). Fitted to improve critical point.
V33 Ionization model=0=Saha model.
V34-V35=0: Reactive chemistry model not used.
Melosh molecular clusters model for the critical point (Melosh fitted values for V36-V43):
V36 Natom=2: number of atoms in molecular clusters
V37 Ebind=4.25 eV: Binding energy
V38 RotDOF=2.0: Rotational degrees of freedom, 2 for diatomic molecule
V39 Rbond=1.5E-8 cm: Length of molecular bond (cm)
V40 VibDOF=1: Numer of vibrational degrees of freedom, 1 for diatomic molecule
V41 Tdebye=2000 K: Vibrational Debye temperature
V42 Mieflag=1: Flag for Mie potential (1) or Morse potential.
V43 aexp=1.55: Power in Mie potential (1 to 2). Fitted to improve critical point
V44 $f{cv}=1.35$: Adjust heat capacity in high temperature limit. $Cv=3f{cv}NkT$.
V45 QCC1: 1.E-30. low density value to transition to ideal gas.
V45 QCC6: 1.E5. high temperature psi value to transition to ideal gas.
V46 to V48=0: Variables not used.
Z=8,12,14: Atomic numbers for Mg2SiO4.
Atomic Fractions=0.571,0.286,0.143: Atomic fractions for Mg2SiO4.
Development Notes¶
STSM 5/16/2019
Setting up development notebooks for pure forsterite.
True Debye temperature for crystalline forsterite is 768+-15 K (Robie et al. 1982).
Triple point of forsterite 5.2e-5 bar, 1890 C (2163 K) (Nagahara et al. 1994).
STSM 5/23/2019
From MELTS: liquid forsterite at 1890°C and 1 bar (Lange): rho = 2687 kg/m^3; solid forsterite at 1890°C and 1 bar (Berman): 2968 kg/m^3. rhol/rhos = 0.90532
Richet et al. 1993 Enthalpy of melting: T=2174(100) K, dS=464(4.3) J/K/kg. dHmelt=1008736 J/kg = 1.0e10 erg/g
Thomas and Asimow 2013 liquid linear shock Hugoniot: rho0=2.597 g/cm3, T0=2273 K, c=2.67 km/s, s=1.64
Enthalpy of formation at 0 K from JANAF: 1.54E11 erg/g. Referenced to atomic gas at STP.
5/26/2019
Phase transition feature in ANEOS leads to a non-physical pressure-temperature discontinuity on the melt curve and dicontinuities in the sound speed and modulus in the liquid. Not using this feature.
5/27/2019
Wide-ranging EOS is a compromise to span low and high-pressure liquid regions and provide a realistic relationship between the entropies on the Hugoniot and the entropies of the low-pressure melt and partial vaporization regions.
6/4/2019
Added section to compare to shock-and-release-stagnation experiments with results from the Z machine.
6/6/2019
Added option to remove the tension region of the table and replace with sublimation.
Added extra grid points in the tension region.
7/10/2019
Updated ANEOS to include a multiplicative scaling factor for the high temperature heat capacity limit. This term $f_{cv}$ is entered in V44. The heat capacity limit is $3f_{cv}NkT$. There are two additional input parameters which define the transition to an ideal gas: V45=QCC1 and V46=QCC6.
7/11/2019
Updated ANEOS for the user-defined heat capacity using the full Debye function.
7/29/2019
Added comparison plots to Tillotson and previous versions of ANEOS for forsterite.
8/2/2019
Removed unpublished data for beta release for GitHub.
10/3/2019
Converted EOS data variables to class structures.
Currently using linear interpolation for the GADGET2 table.
10/4/2019
Finished MDQ and IEP plots.
Added extra gridding around the triple point. Now there is no longer a gap in the specific entropies near the triple point.
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